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Here is a link to the question:Find the indefinite integral?

x^4(5x^5+1)^7 dx

Find the indefinite integral? - Yahoo! Answers

I have posted a link there to this topic so the OP can find my response.

- Thread starter MarkFL
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- Thread starter
- Admin
- #1

Here is a link to the question:Find the indefinite integral?

x^4(5x^5+1)^7 dx

Find the indefinite integral? - Yahoo! Answers

I have posted a link there to this topic so the OP can find my response.

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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.