Integrate cos (lnx) dx Integrating by parts:
I'm having a hard time choosing the $u$, $du$, $v$ and $dv$...
I gave it a shot.
$u = \ln x \implies du = 1/x \ dx$
$v= \  ?$
$dv =  \cos \ dx$

Hint: $\int \cos(\ln(x)) dx= \int \cos(u)xdu=\int  \cos(u)e^{u}du$
