You need to integrate by parts? That is not built-in functionality, as far as I know, but you can write your own rule:
integrateByParts[f_, df_, x_] :=
Integrate[df*g_, {x, a_, b_}] :>
(f*g /. x -> b) - (f*g /. x -> a) - Integrate[f*D[g, x], {x, a, b}];
origIntegral =
Integrate[
Cos[k \[Psi]] D[f[v, \[Psi]], \[Psi], \[Psi]], {\[Psi], 0, Pi}];
ibp = origIntegral /.
integrateByParts[D[f[v, \[Psi]], \[Psi]],
D[f[v, \[Psi]], \[Psi], \[Psi]], \[Psi]] /.
integrateByParts[f[v, \[Psi]], D[f[v, \[Psi]], \[Psi]], \[Psi]]
