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Evaluate the integral.

{eq}\displaystyle \int 3 \tan^2 x \sec^3 x\ dx {/eq}.

Question:

Evaluate the integral.

{eq}\displaystyle \int 3 \tan^2 x \sec^3 x\ dx {/eq}.

Indefinite Integral in Calculus:

Integration techniques can be used to find anti derivative of a trigonometric function.

To solve this problem, we'll use integration by substitution, which is also called u-substitution and we'll also use integral reduction rule : {eq}\displaystyle \int \sec ^{n}x \ dx=\dfrac {\sec ^{n-1}x \sin x}{n-1}+ \dfrac{n-2}{n-1} \int \sec^{n-2} x \ dx {/eq}

Answer and Explanation: 1

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We are given:

{eq}\displaystyle\int 3 \tan^2(x) \sec^3(x) \, \mathrm{d}x {/eq}

Take the constant out:

{eq}=\displaystyle 3 \int \sec^3(x)...

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Work as an Integral

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Chapter 7 / Lesson 9
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Learn the work done formula and understand the application of work integral in the work done formula with examples problems using calculus.


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