# Just another integration problem

• November 21st 2006, 03:19 AM
taryn
Just another integration problem
integral (x^6)ln(x)dx

The thing is... I have the exam in 2 days and this is the main thing I am havin problems with!

I tried makin u=x^6
and then integratin by parts which didnt seem to work!

I ended up gettin (x^6)(lnx)-(6x^5)(lnx^2)
Is this completely wrong... do I continue to integrate... Is there another way to do this?
• November 21st 2006, 03:36 AM
taryn
So another Idea I had was to make u=x^7
and then basically just sub it in! And then using log laws I get that the answer is this

1/49 int lnu du and I can go from there... but is that right and how do I know which to use... is it just trial and error?:confused:
• November 21st 2006, 03:46 AM
malaygoel
Quote:

Originally Posted by taryn
integral (x^6)ln(x)dx

The thing is... I have the exam in 2 days and this is the main thing I am havin problems with!

I tried makin u=x^6
and then integratin by parts which didnt seem to work!

I ended up gettin (x^6)(lnx)-(6x^5)(lnx^2)
Is this completely wrong... do I continue to integrate... Is there another way to do this?

substitute lnx = t

Keep Smiling
Malay
• November 21st 2006, 03:47 AM
galactus
Quote:

Originally Posted by taryn
integral (x^6)ln(x)dx

The thing is... I have the exam in 2 days and this is the main thing I am havin problems with!

I tried makin u=x^6
and then integratin by parts which didnt seem to work!

I ended up gettin (x^6)(lnx)-(6x^5)(lnx^2)
Is this completely wrong... do I continue to integrate... Is there another way to do this?

Use integration by parts:

$u=lnx; du=\frac{1}{x}dx; dv=x^{6}dx; v=\frac{x^{7}}{7}$

$\frac{1}{7}x^{7}lnx-\int\frac{1}{7}x^{7}\frac{1}{x}dx$

$\frac{x^{7}lnx}{7}-\frac{x^{7}}{49}+C$
• November 21st 2006, 03:52 AM
taryn
ahh cool! I got the same answer doin it the other way as well but this way seems just a little bit easier! Thanks for all your help! I really appreciate it!