# Luc's question at Yahoo! Answers regarding an indefinite integral

Staff member

#### MarkFL

Staff member
Re: Luc's question at Yahoo! Answers regarding an indedinte integral

Hello Luc,

$$\displaystyle \int x^4\left(5x^5+1 \right)^7\,dx$$

It we use the $u$-substitution:

$$\displaystyle u=5x^5+1\,\therefore\,du=25x^4\,dx$$

we may rewrite the integral as:

$$\displaystyle \frac{1}{25}\int u^7\,du=\frac{1}{25}\left(\frac{u^8}{8} \right)+C=\frac{1}{200}u^8+C$$

Now, back-substituting for $u$, we may state:

$$\displaystyle \int x^4\left(5x^5+1 \right)^7\,dx=\frac{1}{200}\left(5x^5+1 \right)^8+C$$

To Luc and any other guests viewing this topic, I invite and encourage you to post other calculus problems in our Calculus forum.

Best Regards,

Mark.