# Integrate sin(lnx)dx

1. Feb 9, 2006

### superelf83

we are doing 'integration by parts' right now. but we never learned anything like this. (having a function inside a function).
would u=lnx du=1/x .. v= ??? dv = sin... ????

2. Feb 9, 2006

### d_leet

Let u = sin(ln x)
and dv = dx

It works out very nicely.

3. Feb 9, 2006

### superelf83

hummm.

so...
u=sin(lnt) du=cos(lnt)(1/t)dt
v=t dv=dt

intergration of sin(lnt)dt =
tsin(lnt)- ∫tcos(lnt)(1/t)dt (and then do integration by parts again?)

could you just tell me if i took the derivative of u correctly? thank you so much by the way~ :)

4. Feb 9, 2006

### d_leet

Yea looks right and don't forget to cancel the t and 1/t inside the integral, then do parts again the exact same way and you should get it.

5. Feb 9, 2006

### superelf83

THANK YOU SO MUCH! :) you are so kind. hehehe

6. Feb 9, 2006

### d_leet

No problem glad I could help, and I'll take that to mean that you got the answer lol...