Integration by Parts Questions and Answers

Get help with your Integration by parts homework. Access the answers to hundreds of Integration by parts questions that are explained in a way that's easy for you to understand. Can't find the question you're looking for? Go ahead and submit it to our experts to be answered.

Homework Help Tools
30,000+ Video Lessons
2,000,000+ Questions and Answers
65,000+ Quizzes

Integration by Parts Questions and Answers

Test your understanding with practice problems and step-by-step solutions. Browse through all study tools.

Determine whether the integration formula is correct. x^8\tan^{-1}x\,dx = \dfrac{1}{9}\left(x^9\tan^{-1}x - \int \dfrac{x^9\,dx}{1 + x^2}\right) + C
Evaluate the integral of e^(x^1/3) dx
Evaluate the given integral. int x e^x dx
Evaluate the improper integral or state that it is divergent. \int_{-\infty}^{\infty} 16xe^{-x}\,dx (a) 16 (b) Divergent (c) 0 (d) -16
Evaluate the integral. \int_0^{π} 4t sin 9t dt.
In using the technique of integration by parts, you must carefully choose which expression is u. For the following problem, choose u. Do not evaluate the integral. \int x^7 \arctan(3x)\,dx
Evaluate \int x \arctan 3x \,dx.
Evaluate \int_1^2 (\ln x)^2\,dx.
In using the technique of integration by parts, you must carefully choose which expression is u. For the following problem, choose u. Do not evaluate the integral. \int x^8 \sin(6x)\,dx
Given f(1) = 6,\enspace f(4) = 7,\enspace f'(1) = 4,\enspace f'(4) = 3. Suppose f'' is continuous. Find the value of \int_1^4 xf''(x)\,dx.
Evaluate: int_0^1 t cosh t dt.
Determine whether the integration formula is correct. \int x^2\cos^{-1}3x\,dx = \dfrac{x^3}{3}\cos^{-1}3x + \dfrac{3}{3}\int \dfrac{x^3 \,dx}{\sqrt{1 - 9x^2}} + C
Determine whether the integration formula is correct. \int x^4\sin^{-1}8x\,dx = \dfrac{x^3}{3}\sin^{-1}8x + \dfrac{8}{5}\int \dfrac{x^5 \,dx}{\sqrt{1 - 64x^2}} + C
In using the technique of integration by parts, you must carefully choose which expression is u. Choose u for the following expression. Do not evaluate the integral. \int x^3\ln(6x)\,dx
Evaluate the integral. Integral from 0 to pi/4 of (x sin x)/(cos^3 x) dx.
Evaluate \int x^2 \cdot \sin 2x\,dx. (a) None (b) \dfrac{x^2\cos 2x}{2} + \dfrac{2x\sin 2x}{4} + \dfrac{2\cos 2x}{8} + C (c) \dfrac{-x^2\cos 2x}{2} - \dfrac{2x\sin 2x}{4} + C (d) \dfrac{-x^2\cos 2x...
Evaluate \int \ln(1 + x)\,dx.
Evaluate \int (x \cdot \cos x)\,dx.
Evaluate the following indefinite integral: \int ln(x^2 + 2x + 2) \: dx.
Evaluate the integral. \int \cos \sqrt{x} dx
Evaluate \int e^{5x} \cos (2x)dx.
Evaluate the integral. Integral of e^(-theta) cos 2theta d(theta).
Use the Table of Integrals to evaluate the integral. Integral of (cos^(-1)(x^(-2)))/(x^3) dx.
Evaluate the integral. \int y^2 \sin 3y\ dy
Integral from 0 to 1/3 of xe^(3x) dx = A. 1/9 B. None of these C. 1/4 D. 1/16
(a) Prove the following: \int (\ln x)^n \,dx = x(\ln x)^n - n \int (\ln x)^{n - 1} \, dx (b) Use (a) above to compute the following: \int (\ln x)^3 \, dx
Use the Table of Integrals to evaluate the integral. Integral of (ln(1 + sqrt x))/(sqrt x) dx.
Use the Table of Integrals to evaluate the integral. Integral of sin^2 x cos x ln(sin x) dx.
\int_1^5 t^2 \ln(5t) \, dt = ?
Evaluate the integral. Integral of te^(sqrt t) dt.
Evaluate the integral. Integral from 0 to pi/6 of t sin 2t dt.
What is the antiderivative of the equation \int \left ( \frac{x}{ln}(x) \right ) ?
Evaluate the integral using integration by parts with the indicated choices of u and dv. Integral of theta cos theta d(theta); u = theta, dv = cos theta d(theta).
Evaluate the integral using integration by parts with the indicated choices of u and dv. Integral of x^2 ln x dx; u = ln x, dv = x^2 dx.
Evaluate the integral. Integral of ye^(0.2y) dy.
Evaluate the integral. Integral of sin^(-1) x dx.
Evaluate the integral. Integral of ln(cube root of x) dx.
Evaluate the integral. Integral from 1 to 2 of (ln x)^2/(x^3) dx.
Evaluate the integral. Integral from 1 to sqrt(3) of arctan(1/x) dx.
Evaluate the integral. Integral from 0 to 1 of (x^2 + 1) e^(-x) dx.
Evaluate the integral. Integral from 1 to 3 of r^3 ln r dr.
Evaluate the integral. Integral from 0 to 1 of t cosh t dt.
Evaluate the integral. Integral from 4 to 9 of (ln y)/(sqrt y) dy.
Evaluate the integral. Integral from 0 to 1 of y/(e^(2y)) dy.
Evaluate the integral. Integral from 0 to 2pi of t^2 sin 2t dt.
Evaluate the integral. Integral of x tan^2 x dx.
Evaluate the integral. Integral of z^3 e^z dz.
Evaluate the integral. Integral from 0 to 1/2 of x*cos(pi*x) dx.
Evaluate the integral. Integral of arctan 4t dt.
Use the Table of Integrals to evaluate the integral. Integral from -1 to 0 of t^2 e^(-t) dt.
Evaluate the integral. Integral of theta tan^2 theta d(theta).
Evaluate the given integral. Integral x^3 ln (2x) dx
Evaluate the integral. Integral from 0 to pi of t*cos^2 t dt.
Evaluate the integral. Integral from 1 to 3 of r^4 ln r dr.
Use integration by parts to evaluate the integral. Integral of x*tan^(-1)(x) dx.
Evaluate the integral of (e^(ax))(sin 3x)dx; assume a is a constant.
Use the tabular method to find the integral. Integral x^3 sin x dx
Evaluate the given integral. Integral of xe^x dx.
Evaluate the integral from 0 to 1/2 of t*ln(1 + t) dt.
Evaluate the integral of (ln(9x))/(x^7) dx.
Find the integral using the tabular method. int x^2 sin x dx
Find the integral using the tabular method. int_1^2 x ln x dx
Find the integral using the tabular method. \int (x\sin (x \over 2)) \ dx
Evaluate the integral. integral 3 x e^{-2 x} d x
Evaluate the integral using integration by parts. int e^-3 theta sin 9 theta d theta
Evaluate the integral. int x^2 cos (1 over 4 x) dx
First make a substitution and then use integration by parts to evaluate the integral. Integral of cos(ln x) dx.
Find the integral from 1 to 5 of w^2 ln(w) dw.
Find the integral of 2^x sin x dx.
In using the technique of integration by parts, you must carefully choose which expression is u. For the following problem, choose u. Do not evaluate the integral. Integral of e^(3x) sin(2x) dx.
In using the technique of integration by parts, you must carefully choose which expression is u. For the following problem, choose u. Do not evaluate the integral. Integral of y^3 cos y dy.
In using the technique of integration by parts, you must carefully choose which expression is u. For the following problem, choose u. Do not evaluate the integral. Integral of x^3 ln(x) dx.
Evaluate: the integral from 1 to e of (ln x)/(x^2) dx.
Evaluate. int limits_0^pi/6 23 theta sqrt 1 - cos (2 theta)d theta
Evaluate the integral using integration by parts. int limits_1^e^5 x^5 ln (x) dx
Find the integral of sec^3 x dx.
Find the integral x^{3} e^{3 x} d x with the help of partial integral.
Find the integral from 0 to 1 of sqrt(x) (x + 1) dx.
Find the integral from 0 to 1/3 of xe^(3x) dx.
Use integration by parts to Evaluate: \int \ln 13 x dx
Evaluate the following integral: integral of x sin(2x) dx.
The integral of ln(x) dx = 1/x + c. A. True B. False
Evaluate the integral using integration by parts technique. int_0^4 x root 3 of x + 3 dx
Evaluate. int e^t sin (alpha t - 3) dt
Determine if the following statement is true or false. For a true statement, explain why it is true. For a false statement give an example to show why it is false. \int \frac{f(x)}{g(x)} dx = \fra...
Compute the following integral. int_0^+infty (1 - x) e^- x dx
Find integral of (cos x/ln x)dx - integral of (((sinx)(1/x))/(ln x)^2)dx
Evaluate the integral. (ln t/t^2)dt
State, with reason, whether the following statement is true or false: integral of f(x)dx = xf'(x) - integral of xf'(x)dx.
Evaluate the following indefinite integral: \int x \: e^{-2x} \: dx.
Evaluate the integral.p5 ln p dp
Evaluate the integral. sinh mt dt
Evaluate the integral.xe2x/(1+2x)2
Evaluate the following integral using integration by parts. (x^4 ln x) dx
Evaluate the integral using integration by parts technique : (x cuberoot(x + 2))dx from 0 to 3
Evaluate using integration by parts. \int x \cos (x) dx
Evaluate the integral. xsecxtanx
Integrate the following. int e^x (1 + x ln (x)) over x
Evaluate the integral.tan2xsecxdx
Evaluate the integral.xsecxtanxdx
Evaluate the integral. int log_2 x^3 over 4x^2 dx
Evaluate by using parts. \int x^3 \ln (x) dx
Find the integral. integral e^{2 x} sin(2 x) d x
Use integration by parts to compute the following: int e^x sin x dx
Use integration by parts to compute the following: int x sin x dx
Use integration by parts to compute the following: int limits_1^e x^2 ln x dx
Use integration by parts to compute the following: int limits_0^1 t^2 e^t dt
Evaluate the following integral. \int \sin x \ln (\cos x) dx
Evaluate the following integral. \int e^{2x} \sin (3x) dx
Find the integral of (1 + 3x) e^(-x) dx.
Suppose that f(1) = -3, f(4) = -8, f'(1) = 10, f'(4) = -4, and f'' is continuous. Find the value of the integral from 1 to 4 of x*f''(x) dx.
Evaluate the integral using integration by parts. \int x e^{3x} dx
Evaluate the following integral. \int \ln (1 + 4x^2)dx
Evaluate the integral of (xe^x)/(1 + x)^2 dx.
Find the integral from 2 to 5 of (t^4)(ln 4t)dt
Evaluate the following integral. int x sin (2x) dx
Evaluate the integral. int 5 ln (x + 7) over x^2 dx
Solve the integral. \int \frac{\ln x}{x^2} dx
Integrate the following a) integral x arc tan x d x
Find the indefinite integral. Integral of 3 arctan x dx.
Evaluate the integral of x^2 e^(4x) dx.
Find the integral of e^(8x) sin(3x) dx.
Evaluate the indefinite integral. int x^2 e^-x dx
Find the integral. int x^2 sin^2 x dx
Evaluate the following trigonometric integral. Integral of cos^4 2theta d(theta).
Integrate the following function. int (x^2 - 1) e^x dx
Solve the indefinite integral. \int x^2 \exp(-x) \; dx
Evaluate the integral using integration by parts. int 6x^4 e^-4 dx
Evaluate the integral from 1 to 2 of x^2 ln x dx.
Evaluate the integral. int_0^pi/2 e^2x sin x dx
Suppose that f(1) = 4, f(4) = 8, f(1) = 3, f'(4) = 4, and f" is continuous. Find the value of the integral from 1 to 4 of (x)(f"(x)) dx.
Evaluate the integral. int 2 ln (x + 5) over x^2 dx
Evaluate the following integral using integration by parts. int_0^pi x sin x dx
Evaluate the integral using integration by parts. int x sin x dx
Solve the following integral. integral x^{2} e^{3 x} d x a) 0 b) 5 e^{3} / 27 - 2 / 27 c) 5 e^{3} / 27 d) 5 e^{3} / 3
Evaluate the integral from pi/4 to pi/3 of (sec^3 theta)/(tan theta) d(theta).
Evaluate the following integral using integration by parts. a) integral e^{x} cos 2 x d x
Evaluate int t^2 ln t dt.
Evaluate int 4x e^2x dx.
Evaluate the integral. int ln (2x) over x^2 dx
Evaluate the integral. int x^2 e^-x dx
Evaluate. \int x \sin(3x - 2) dx
Evaluate the integral. int t^4 ln (t) dt
Evaluate the integral of x^3 sin 5x dx.
Evaluate the integral of e^(-3theta) cos theta d(theta).
Find the integral of e^(3x) cos(2x) dx.
Use integration by parts to evaluate the integral of x sec x tan x dx. (Hint: the integral of sec x tan x dx = sec x + C. )
Given a = 2, b = 8, c = 9. Find the following indefinite integral: integral of e^((a + 1)x) cos((b + 1)x) dx.
Find the integral of x^3 ln x dx.
Find the integral of e^(sqrt x) dx.
Evaluate the integral. int 13e^x sin x dx
Evaluate the integral. int (ln 4x)^2 dx
Compute the integral using partial integration a) integral z^{3} e^{3 z} d z
Evaluate the integral (cos x)(ln (sin x)) dx
Evaluate the integral from 1 to 2 of (x^4)((ln x)^2) dx
Evaluate the integral. \int s{6^s} ds
Find the following limit. \lim \limits_x \to 1 (x + 3 \over x - 1)^{x + 3}
Integrate the following function by parts. y = x cos x
Suppose f(1)=3 and f(7)=-5 while g(1)=3 and g(7)=-2. Given that \int(f(x})g'(x)dx
Evaluate the indefinite integral (x^3 sqrt(x^2 + 1) dx
Solve the integral \int \frac{\sin (\frac{1}{x})}{x^3} dx
Use integration by parts to evaluate the given integral
Find the constant A,B,C,D,E such that integral x^4e^x is
Evaluate: int e^{5x}cos 8x dx
Evaluate the integral of 20x e^{4x} dx.
Evaluate the following integral. Simplify as much as possible. \int t \sin (2t) dt
Compute the following integral with respect to x. integral x^2 cos (2x) dx
Evaluate the following integral using Integration by Parts: integral of e^x sin x dx.
If g(1) = -1, g(5) = 8, and integral from 1 to 5 of g(x) d(x) = -7, evaluate the integral from 1 to 5 of x*g'(x) dx.
Evaluate the integral. integral 0 to infinity e^(-x) sin x dx
Determine the integral: Integral sin x ln(1+sin x) dx
Evaluate the integral: Integral square root of{x} cdot ln x dx
Evaluate the integral using integration by parts where possible. Integral x^5 ln x dx
Evaluate the integral using integration by parts where possible. integral x(x+5)^6 dx
Find the integral using integration by parts. Integral 3x tan^{-1} (x) dx
For each integer, we put In. Deduce the formulas.
Evaluate the integral \displaystyle{ I = \int x \cos(4x) \; \mathrm{ d}x. }
Evaluate the indefinite integral \displaystyle{ I = \int x^3 e^{ x^2} \; \mathrm{ d}x. }
Consider a function f (x) = 0, 0 less than or equal to x less than or equal to 1 2 x - 2, 1 less than x less than or equal to 2. In the Fourier Series the constant term b_2 = ____.
If f(x) = x cosx, -pi less than equal to x less than equal to pi then find the b1 Fourier series.
Evaluate the following integrals:- (a) x3sin(2x)dx (b) cos20 x sin3xdx
Evaluate the indefinite integral. Integral x^(1/3) ln (x) dx
Evaluate the indefinite integral. Integral x sin 7x dx
Obtain reduction formula and use it to compute integral_0^pi / 2 cos^n (x) dx, n = 0, 1, 2, 3, . . .
Integrate: int x sqrt{3-x} dx
Integrate: int; x sin x dx
Evaluate the following integral using integration by parts: \int 6xe^{-5x} \: dx.
Evaluate the indefinite integral. int x(4x+5)^8 dx
Evaluate the following integral: \int x\: sin(5-x) \: dx.
Evaluate integral 0^pi x sin 2x dx
Evaluate the following integral. integral x^3 sin (2 x) dx
Evaluate the following integral. \int \cos (\sqrt{x}) dx
Evaluate the following integral. \int \frac{\ln x}{\sqrt x} dx
Evaluate the integral. integral from a to b sin^(-1)x dx where a = -0.8 and b = 0.1.
Evaluate the following integral: xsec2xdx
Show the average value of inetgarl_{0}^{e-1} 2x ln(1+x) dx is 1/2(e-1)^2+e-2.
Find r (t) if r'(t) = t^3 i + e^t j + 2 t e^2 t k and r(0) = i + j + k.
Use Integration by parts to solve the following integrals. Show all your work, including the steps to find all functions and their derivatives or antiderivatives in the integration by parts steps,...
Find A, B, C, D and E to complete the solution of integration x4e(2x)dx = e(2x)(Ax4+Bx3+Cx2+Dx+E)+c
Evaluate the integral, 3/x(x-1)3dx.
Use integration by parts to evaluate the following integral 0^T b te^-rt dt
Use integration by parts to evaluate the following: integral x^3 e^2x dx
Use integration by parts to evaluate the following: integral fraction 1 x ln x dx
Find the indefinite integral of dx/x^2-2x+5.
Evaluate the integral. integral_0^square root 3 3 tan^-1 (x) dx
Use integration by parts to evaluate the following: \int 4x^3 \: ln(5x) \: dx.
Evaluate the following definite integral: \int_{0}^{2 \pi} cos(5x) \: cos(7x) \: dx.
For a non-negative integer n greater than or equal to 0, J_n = integral (ln x)^n dx. Express J_n in terms of J_n-1 for n greater than or equal to 1. Hence, find J_3.
Evaluate the following indefinite integral \displaystyle{ \int \cos^{ 1} (x) \; \mathrm{ d}x. }
Use the FTC, calculate int In(x) dx.
Verify that F(x) = x ln(x)-x is an antiderivative of ln(x).
Use integration by parts to evaluate the following: \int e^x \: sin(x) \: dx.
Use integration by parts to evaluate the following: \int \dfrac{ln(x)}{x^2} \: dx.
Evaluate the integral. integral 5 x e^-3 x dx
Evaluate the integral. integral x sec^2 (x) dx
Find the following integration by parts. integral (1 + 3 x^3) ln (x) dx
Evaluate the following integral. integral e^2 x cos (1 / 3 x) dx
Find the indefinite integral. integral fraction ln x x^3 dx
Find the indefinite integral. integral e^- 3x sin 5x dx
Using integration by parts, evaluate the integral of 5x cos(8x) dx.
Evaluate the integral. integral_0^1 cos (pi x) e^x dx
Use integration by parts to evaluate integral 5 x^4 ln (7 x) dx.
Evaluate the integral by parts: integral (1+3x^2) ln (x) dx.
Evaluate the integral \displaystyle{ I = \int\limits_0^1 xe^{3x} dx. }
Determine the integral \displaystyle{ I = \int (x^2 4) \cos(2x) dx. }
Evaluate the integral \displaystyle{ \int\limits_1^2 \dfrac{ \ln(t)}{t^2} dt. }
Evaluate the definite integral \displaystyle{ \int\limits_1^e 2x^3 \ln(x) dx. }
Evaluate the integral \displaystyle{ \int\limits_1^2 5 \ln(2x) dx. }
Evaluate the integral: integral Square root of{x} ln (x) dx.
Let a greater than 0. Suppose f(0) = g(0) = 0 and f'' and g'' are continuous. Show that integral_{0}^{a} f(x) g''(x) dx = f(a) g'(a) - f'(a) g(a) + integral_{0}^{a} f''(x) g(x) dx.
Evaluate the integral. integral fraction pi 2 ^pi pi - x sin nx dx
Evaluate the integral. integral fraction pi 2 ^ pi pi - x cos nx dx
Evaluate the following integral. integral from 0 to 1 cos^-1 x dx
Evaluate the following integral: \int x^2e^{-2x} \: dx.
Evaluate the following integral: \int x^2 \: cos(2x) \: dx.
Compute the following integral. integral x^3 e^x dx
Evaluate the following integral by utilizing the integration by parts technique. integral tan^-1 (5 t) dt
Use integration by parts to find the most general anti-derivative of integral x^2 cos(4x) dx.
Use integration by parts to evaluate the following integral. Integral of (2x - 1) ln(7x) dx.
Integrate integral x^2 cos 7x dx
The integral converges. Evaluate the integral. integral - infinity^2 theta e^theta dtheta
Evaluate the integral. Use C for constant of integration integral fraction square root 81 x^2 + 16 x^2 dx
Use integration by part to evaluate integral e^8x sin (e^4 x) dx.
Evaluate the integral. Use integration by parts integral ln square root t dt
Assume f (x) is a function with continuous derivatives and f (2) = 3, f (3) = 3, and f' (3) = 0. Compute the following definite integral: integral_2^3 (-2 x + 4)f'' (x) dx
Evaluate the integral using integration by parts:\\ I = \int \begin{bmatrix} x^2 \cdot cos(\pi x) \end{bmatrix} dx
Find the integral of 5x^2 sin(8x) dx using integration by parts.
Find integral fraction 4 ln x x^3 dx. Use integration by parts.
If g 1 = -5, g 5 = 4, and integral 1^5 g x dx = - 9, evaluate the integral integral 1^5 x g' x dx.
Evaluate. The integral from 1 to 4 of x^(3/2) ln x dx.
Evaluate Use C for the constant of integration. integral 3x^7 cos x^4 dx
Evaluate the integral using Integration by Parts, substitution, or both if necessary. Use C for the constant of integration. integration fraction ln ln 2x dx x
Find the solution of the differential equation that satisfies the given initial condition. x^2y' + 2xy = ln x y 1 = 2
Find the particular solution of the first-order differential equation: dy dx = x^2 e^3x +2x^2e^3x y satisfying the boundary condition y(0)= fraction 1 2
Evaluate the integral. 3x ln(1 + x)dx
Integrate the integral of x^5 ln 3x dx.
Integrate the integral of e^(3x) sin 2x dx.
If n \gt 2 is an integer, show that \\ \int \cos^n (x)dx = \dfrac{1}{n}\cos^{n-1}(x)\sin(x) + \dfrac{n-1}{n} \int \cos^{n-2}(x)dx.
Evaluate the integral. integral 0^1 -2x5^x dx
Calculate the indefinite integral. (Use C for the constant of integration.) integral t e^6 t dt
Evaluate the integral. integral 6 y^3 e^y dy
Evaluate integral x cos(138 x) dx.
Integrate the following and don't simplify. integral (x^2 - 3 x - 4) e^-2 x dx
Evaluate the following integral: \int e^x \: sin(x) \: dx.
Evaluate the following integral: \int tan^{-1} (y) \: dy.
True or False: By using integration by parts, the integral is evaluated as \int_2^4 3 x \ln (x) dx = 20.1.
Evaluate the following integral: \int_{0}^{\pi/2} sin^{11} (\theta) cos^5(\theta) \: d\theta.
Evaluate the integral. integral from 0 to 1 (x^2 + 4)e^-x dx
Find (f^-1) (0). f(x) = integral_2^x square root 5 + t^2 dt
Calculate the given integral. integral of e^x sin x dx
Calculate the given integral. integral of (x^2 + 4x) cos x dx
Evaluate the integral. integral square root 36 x^2 - 25 / x^3 dx
Show that \int_0^1 (1 - x^2)^n \ dx = \dfrac {2^{2n}(n!)^2} {(2n + 1)!} Hint: Start by showing that if In denotes the integral, then I_{k+1} = \dfrac {2k + 2}{2k _ 3} I_k
If f(0) = g(0) = 0 and f'' and g'' are continuous, show that the integral from 0 to a of f(x)g"(x)dx = f(a)g'(a) - f'(a)g(a) + the integral from 0 to a of f"(x)g(x)dx
Use integration by parts to prove the reduction formula. \int\sec^nx\;dx=\frac{\tan x \sec^{n-2}x}{n-1}+\frac{n-2}{n-1}\int\sec^{n-2}x\;dx\quad (n\neq 1)
Use integration by parts to prove the reduction formula. \int \tan^n x\; dx = \frac{\tan^{n-1}x}{n-1}-\int \tan^{n-2}x\; dx\quad (n\neq1)
The function is defined as f(x) = integral_{0}^{infinity} t^xe^{-t} dt. Calculate f(3), f(4), and f(5).
Evaluate the integral. integral square root 9 x^2 + 4 / x^2 dx
Evaluate the integral. integral arctan square root x / square root x dx
Evaluate the integral. integral_0^1 x^4 e^-x dx
Find the integral of x^4 e^x dx.
Show that integral_0^infinity x^2 e^-x^2 dx = 1 / 2 integral_0^infinity e^-x^2 dx.
Evaluate the integral. \int_0^{\pi /8} {\arctan 2x \ dx}
Evaluate the integral. \int {{e^t}} \sin \left( {\alpha t - 3} \right)dt
Approximate the definite integral. integral_0^3 x sin x dx
Suppose that f(1) = 2, f(4) = 7, f'(1) = 5, f'(4) = 3, and f'' is continuous. Find the value of \int_{1}^{4} xf''(x) dx.
For what values of a is \int_{0}^{\infty} e^{ax} \cos x dx convergent? Evaluate the integral for those values of a.
State the rule for integration by parts. How is it used in practice?
If n is a positive integer, prove that integral_0^1 (ln x)^n dx = (-1)^n n!.
Evaluate the following integral. Integral of 2e^(2x) x^3 (x + 2) dx.
First, make a substitution and then use integration by parts to evaluate the integral. \displaystyle \int e^{\sqrt{x}}\ dx
Use integration by parts to evaluate the following integral: Integral of 3x^2 ln(x^3) dx. Identify the values that need to be used for u, du, dv, and v as well as the final value for the integral.
Evaluate the integral. \int_0^{\pi /6} {t\sin 2t \ dt}
Find the indefinite integral and check the result by differentiation. \int 4\pi y(6+y^{3/2})\;dy
Use integration by parts to prove the reduction formula. \int {{x^n}{e^x} \ dx = {x^n}} {e^x} - n\int {{x^{n - 1}}{e^x} \ dx}
Find the integral: (cosh x)/(sinh x) dx
Evaluate the following integral. \int x \sin x \cos x \; dx
If integral_0^pi / 4 tan^6x sec x dx = I, express the value of integral_0^pi / 4 tan^8x sec x dx in terms of I.
Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. \int \textrm{ln}\;x\;dx=(1/x)+C
Calculate the value of the multiple integral. double integral_D y / {1 + x^2} dA, where D is bounded by y = square root x, y = 0, x = 1.
Evaluate the integral. \int x^2\;\textrm{sinh}\;mx\;dx
Evaluate the integral. \int \textrm{sin}\sqrt{at}\;dt
Evaluate the integral. \int \sqrt{x}\;e^{\sqrt{x}}\;dx
Evaluate the integral. Integral of (tan^(-1) x)/(x^2) dx.
Evaluate the integral. Integral of ln(x + sqrt(x^2 - 1)) dx.
Evaluate the integral. Integral from 1 to 4 sqrt(y) ln y dy.
Evaluate the integral. integral x sin^2 x cos x dx
Evaluate the integral. integral_1^5 M / {e^M} dM
Evaluate the integral. integral_0^2 y sinh y dy
Evaluate the integral. integral_1^2 w^2 ln w dw
Evaluate the integral. integral_0^1 (x^2 + 1) e^{-x} dx
Evaluate the integral. integral_0^{1/2} x cos pi x dx
Evaluate the integral. integral e^{-theta} cos 2 theta d theta
Evaluate the integral. integral e^{2 theta} sin 3 theta d theta
Evaluate the integral. integral z^3 e^z dz
Evaluate the integral using integration by parts with the indicated choices of u and dv. integral square root x ln x dx; u = ln x, dv = square root x dx
Evaluate the integral. integral (x - 1) sin pi x dx
Evaluate the integral. integral (x^2 + 2 x) cos x dx
Evaluate the integral. integral t^2 sin beta t dt
Evaluate the integral. integral cos^{-1} x dx
Evaluate the integral. integral e^x cos x dx
Use integration by parts to evaluate the integral. integral x tan^{-1} x dx
First make a substitution and then use integration by parts to evaluate the integral. Integral from 0 to pi of e^(cos t) sin 2t dt.
First make a substitution and then use integration by parts to evaluate the integral. Integral of (arcsin(ln x))/x dx.
Evaluate the integral. \int_0^{\infty} xe^{- \frac {x}{4}} dx
Evaluate the iterated integral. \int_0^{\pi/2} \int_0^x x \sin y \ dy \ dx
Evaluate the integral. \int_{1}^{\sqrt{3}}\frac{\sqrt{1+x^2}}{x^2}dx
Evaluate the integral. \int \frac{\textrm{ln}(x+1)}{x^2}dx
Evaluate the integral. \int \frac{(x-1)e^x}{x^2}dx
Evaluate the integral. \int_{0}^{\pi}t \; \textrm{cos}^2t \; dt
Evaluate the integral. \int x \; \textrm{sec}x \; \textrm{tan}x \; dx
Evaluate the integral. \int \textrm{ln}(1+x^2)\;dx
Evaluate the integral. \int_{1}^{2} \frac{(\textrm{ln} \; x)^2}{x^3}dx
Evaluate the integral. \int_{0}^{\pi} x \; \textrm{sin}x \; \textrm{cos}x \; dx
Evaluate the integral. \int x \; \textrm{tan}^2x \; dx
Evaluate the integral. \int ye^{0.2y}dy
Evaluate the integral. \int x \; \textrm{cos} \; 5x \; dx
Evaluate the integral. \int \textrm{tan}^{-1}2y \; dy
Evaluate the integral. \int (\textrm{ln} \; x)^2 \; dx
Evaluate the integral. \int t^4 \textrm{ln}t \; dt
Evaluate the integral. \int_{0}^{\pi/4}\frac{x \; \textrm{sin} \; x}{\textrm{cos}^3x}dx
Evaluate the integral. \int x \; \textrm{sin}x \; \textrm{cos}x \; dx
Evaluate the integral. \int \textrm{cos} \; \sqrt{t} \; dt
Evaluate the definite integral. Integral from -pi/3 to pi/3 of x^4 sin x dx.
Use the Integral Test to determine whether the series is convergent or divergent. Sum of n^2 e^(-n^3) from n = 1 to infinity.
Evaluate the integral. integral x tan^2 x dx
Evaluate the integral, or show that it is divergent: \int_{1}^{\infty} \dfrac{ln(x)}{x^4} \: dx.
Evaluate the integral, or show that it is divergent: \int_{0}^{4} \dfrac{ln(x)}{\sqrt{x}} \: dx.
How do you integrate tan(4x)?
Evaluate int 4t^4/(1 + t^4)^2 dt using integration by parts.
Suppose that f\left( 1 \right) = 4,f\left( 4 \right) = 6,f'\left( 1 \right) = 6,f'\left( 4 \right) = 3, and f'' is continuous. Find the value of \int_1^4 {xf''\left( x \right)dx}.
Compute the following integral. integral_0^{infinity} e^{-s t} t^3 dt
Use integration by parts to establish the reduction formula for \int x^n \; cos(x) \; dx.
Evaluate the following integral. I = integral (6 x + 5) e^{2 x} dx
Evaluate the integral. integral_0^{1 / {square root 2}} 2 r sin^{-1} (r^2) dr
Evaluate the following integral. integral 18 x^2 ln x dx
Evaluate integral x cos(106x) dx.
Solve the following integral: \int_{- \infty}^{\infty} e^{-|x|} \: cos(x) \: dx.
Solve the following integral: \int_{1}^{a} x \: ln(x) \: dx, where a \in \mathbb{R}.
Evaluate the integral. (Use C for the constant of integration.) \int 7x cos(2x) dx
Evaluate the integral. integral x cos (5 x) dx
\int xcos(3x)dx = ?
Find the indefinite integral using integration by parts. integral x^2 e^{3 x} dx
Evaluate the indefinite integral. integral x e^{4x} dx
Determine the integral (if possible) using integration by parts. integral (2 x + 5) (x + 1)^{1 / 2} dx
Solve the integral. integral x^2 4^{-x} x dx
Evaluate the following integral. int_0^{\pi} int_0^x sin(x) dydx
Using integration by parts, evaluate integral x^2 . ln (2x) dx.
Integrate the following indefinite integrals: A) integral of x^5 tan^(-1) x^6 dx B) integral of dx/(sqrt(24 + 6x - 9x^2)).
Can you evaluate the integral \int \frac{dx}{x \ln x} by applying integration by parts, where u = \frac{1}{\ln x} and dv = \frac{dx}{x}? Why?
Integral cos square root x dx = 2 square root x sin square root x + 2 cos square root x + C. a. True. b. False.
Evaluate the integral integral {dx} / {x ln x} by applying integration by parts, where u = 1 / {ln x} and dv = {dx} / x? Why?
Evaluate the integral integral_0^1 x^{-1/3} ln x dx by applying a) integration by parts and b) u-substitution where u = x^{2/3}.
Evaluate the following integral. integral x arcsin x dx
Evaluate the following indefinite integral. integral e^{-2 x} sin 3 x dx
Evaluate the following indefinite integral. \int e^{-2x} sin 3x dx
Evaluate the following indefinite integral. integral e^{-2x} sin 3x dx
Evaluate the integral. integral_0^{pi / 4} x sec^2 (x) dx
Use integration by parts to integrate the following. integral 3x . sin (2 x) dx
Evaluate the integral using integration by parts. integral e^{-x} sin 4 x dx
Evaluate the integration. integral x sec^{-1} x dx
Evaluate the integral. integral {sin (1 / x)} / {x^5} dx
If f(0)=5, f(1)=2, f'(0)=1, f'(1) =3 then what is int_{0}^{1} x f'' (x) dx.
Evaluate the limit. integral_6^0 (2 + 5 x) e^{1 / 3 x} dx
Evaluate the following using integration by parts (c) \int z \sin(z)\; dz (e) \int x \sec^2x\;dx
Find the most general antiderivative of the function. f(x) = \frac{e^{x} + 2 cos x - 3}{{(cos^{2} x)}}
Evaluate integral_0^1 e^{2 x} sin (2 x) dx. Round your answer to three decimal places.
Find the indefinite integral. integral e^{6 s} cos (3 s) ds
Find the indefinite integral. integral {2 x^2} / {e^x} dx
Use integration by parts to evaluate the integral. integral sin (ln (3 x)) dx
Find a reduction formula for the following integral I_{n} = \int^{\frac{\pi}{2}}_{0} x^{n} sin(x) dx
Sketch the region enclose by the following: y = 2x, \; y = 4x^2. Then, find the area of the region.
The general form of an antiderivative of the function f(x) = csc(x)(9csc(x) - 4 cot (x)) is F(x) = _____ + C. (Do not include the integration constant in the answer.)
Evaluate by integration by parts. integral (1 + x^2)x^5 dx
Use a Laplace transform table to compute Laplace transforms. Find the Laplace transform of the following functions. a) u 1 ( t ) + 2 u 3 ( t ) 6 u 4 ( t ) b) f ( t ) = { 0 , t 1 t 2 2 t +...
Evaluate the following integral using integration by parts. integral 7 x e^{2 x} dx
Evaluate integral x / {square root {x + 5}} dx using integration by parts.
Evaluate the following integral using integration by parts. integral {ln x} / {x^9} dx
Evaluate the following integral using integration by parts. integral_1^{e^5} x^3 ln x dx
Evaluate the following integral using integration by parts. integral_0^pi 8 x sin x dx
Create an account to browse all assets today
Support