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

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MarkFL

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Feb 24, 2012
13,775
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MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
Re: Luc's question at Yahoo! Answers regarding an indedinte integral

Hello Luc,

We are asked to evaluate:

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

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.