Thread: Just another integration problem

1. 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?

2. 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?

3. 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

4. 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:

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

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

$\frac{x^{7}lnx}{7}-\frac{x^{7}}{49}+C$

5. 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!