Stuck on an Integration

**Spoolx** · January 1st 2011, 05:05 AM

$\int x^4 lnx$

So I used integration by parts
$u=lnx \ du= \frac1x \ dv= x^4 \ v=\frac15 x^5$

so using the formula
$UV-\int VdU$

I get
$lnx \frac15 x^5 - \frac15 \int \frac{x^5}x$

Here is where I get stuck, I am not sure how i should approach the integration. If I had the reciprocal it would be no problem.
$\int \frac{x^5}x$

any help is appreciated, thanks!

**Soroban** · January 1st 2011, 05:17 AM

Hello, Spoolx!

Happy New Year!

Don't kick yourself too hard . . .

$\displaystyle\int \frac{x^5}{x}\,dx$

Here is where I get stuck.

. . $\dfrac{x^5}{x} \:=\:x^4$

**Spoolx** · January 1st 2011, 05:18 AM

Originally Posted by Soroban

Hello, Spoolx!

Happy New Year!

Don't kick yourself too hard . . .

. . $\dfrac{x^5}{x} \:=\:x^4$

wow.. I cant believe I missed something that simple, sometimes when you try too hard you miss the easiest things...
Thanks a bunch!

Happy New Year to you also!

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