I am trying to do the integration on the picture (int1). V,omega,theta,rhotræ,ix,iy,ixy,E,R are constants. a(r),å(r),FL(r),FD(r) are splines. It seems to run forever without any error. I have tried a simpler version to figure out if the problem has to do with the splines or the arctan. They can run independently but not when combined. (int2). I use an i7 6700k. I am fine with an aproximated answer within a couple %.