Integrate {eq}\displaystyle \int \frac {x^4}{3x^5 - 7} \ dx {/eq}

Question:

Integrate

{eq}\displaystyle \int \frac {x^4}{3x^5 - 7} \ dx {/eq}

Integration by Substitution:

To do integration by substitution we must choose an expression of {eq}x {/eq} to set equal to {eq}u. {/eq} Then we must rewrite the entire integral in terms of {eq}u, {/eq} including the {eq}dx {/eq} term. A good choice of {eq}u {/eq} will make it so that when the integrand is rewritten it is easy to integrate.

Answer and Explanation: 1

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Here we will let {eq}u=3x^5-7. {/eq} Then {eq}du=15x^4dx\Longrightarrow \dfrac{1}{15} du=x^4dx, {/eq} so we can rewrite the integral as ...

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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.