[?] Calculate the following 2-equation integral?

Questions
1

QQ图片20181221212335.png
QQ图片20181221212335.png640×194 4.92 KB

How to integrate eq2 further?

Thanks.

2

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]]
3

I get it. Thank you. Merry Christmas.

4

Please do not post images of Mathematica code; use text that can be copied and pasted directly into a notebook (indent each line of the code at least 4 spaces).