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Find the integral. Integral of (sqrt(x^3 + 3))/(x^11) dx.

Question:

Find the integral.

{eq}\int \sqrt{x^3 + 3}x^{11} \, \mathrm{d}x {/eq}

Evaluating integrals by substitution:

Substitution is a technique based from chain rule. In this problem, the inside of the square root will give the best substitution.

If given an integral in the form {eq}\displaystyle \int g'(x)f(g(x)) dx {/eq}, use the substitution {eq}u = g(x) {/eq} to reduce the integral to {eq}\displaystyle \int f(u) du {/eq}.

Answer and Explanation: 1

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{eq}u = x^3 + 3 \\ du = 3x^2 dx \\ \displaystyle \frac{du}{3} = x^2dx \\ \displaystyle \frac{du}{3}(x^9) = x^11dx \\ \displaystyle...

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How to Solve Integrals Using Substitution

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Chapter 13 / Lesson 5
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Explore the steps in integration by substitution. Learn the importance of integration with the chain rule and see the u-substitution formula with various examples.


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