Integrate sin(lnx)dx: Integration by Parts Help

[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... ?
please help.

 

[d_leet]

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... ?
please help.

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

It works out very nicely.

 

[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~ :)

 

[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.

 

[superelf83]

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

 

[d_leet]

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

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