# 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.

Become a Study.com member to unlock this answer!

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 ...