integrals

The integral can be evaluated by substituting, cosx = (e^ix + e^-ix)/2, and of the difficulty level which is not expected.

The solution involves polylogarithmic function, Li_s(z).

The solution is,

x²i/2 - xlog(1+e^2ix)+xlog cosx + i Li_s(2,-e^2ix) + C

Regards,

Team,

TopperLearning.