How do I evaluate the indefinite integral ∫(sin(ln(x))/(x))dx ?

Answer 1

If I'm reading the question correctly, you should be able to use simple u substitution. If u=lnx, then du=(1/x)dx. So it become ∫sin(u)du, which is much easier to integrate. I hope this helps!

Answer 2

u= lnx

du= dx/x

Ssin(lnx)dx/x

=Ssinu du

= -cosu + C

= -cos(lnx) + C