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Find the integral.

{eq}\displaystyle \int x^2 \csc^2 (2x^3 ) \ \mathrm{d}x = {/eq}

Question:

Find the integral.

{eq}\displaystyle \int x^2 \csc^2 (2x^3 ) \ \mathrm{d}x = {/eq}

U-Substitution:

To get the value of the given indefinite integral, we must apply a substitution.

We call this method of employing a substitution into an integral u-substitution.

Answer and Explanation: 1

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Using the substitution {eq}u = 2x^3 {/eq}, solve for {eq}\mathrm{d}x {/eq}:

{eq}\begin{align*} \displaystyle u& = 2x^3\\ \mathrm{d}u& =6x^2 \...

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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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