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

[MarkFL]

Here is the question:

Find the indefinite integral?

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

Here is a link to the question:

Find the indefinite integral? - Yahoo! Answers

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

 

[MarkFL]

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

Hello Luc,

We are asked to evaluate:

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

It we use the $u$-substitution:

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

we may rewrite the integral as:

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

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

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

To Luc and any other guests viewing this topic, I invite and encourage you to post other calculus problems in our http://www.mathhelpboards.com/f10/ forum.

Best Regards,

Mark.