Integration by substitution then parts

[Guest]

The integral of sin(ln(x))dx

u=ln(x)
du=1/x dx
xdu=dx - This seems very wrong!

-cos(u)du

x-cos(ln(x))+C

I get the feeling I've done this incorrectly. There are no parts here. Can someone straighten me out.

Thanks

 

[pka]

You can do this by using parts.
Let u=sin(ln(x)) and dv=dx.
Do it twice. Then you can add to both sides and divide by 2.