∫ln⁡(tan⁡x)sin⁡x⋅cos⁡xdx, is equal to

I=∫ln⁡(tan⁡x)sin⁡x⋅cos⁡xdx, let t=ln⁡(tan⁡x)⇒ dtdx=sec2⁡xtan⁡x⇒dt=dxsin⁡x⋅cos⁡x∴ I=∫tdt=12t2+C=12(ln⁡(tan⁡x))2+C