定积分!求数学大神解答!

原式=∫ x/2(cosx)^2 dx
=1/2∫ x(dtanx)
=1/2*[ xtanx-∫tanxdx]
=1/2*[xtanx-∫sinx/cosx dx]
=1/2*[xtanx+∫d(cosx)/cosx]
=1/2*[xtanx+ln|cosx|]
=1/2*[π/4-ln√2]
=π/8-1/4*ln2