∫cos⁡x−1sin⁡x+1exdx is equal to

∫cos⁡x−1sin⁡x+1exdx=∫cos⁡x1+sin⁡xexdx−∫11+sin⁡xexdx=(cos⁡x)ex1+sin⁡x−∫−(1+sin⁡x)sin⁡x−cos2⁡x(1+sin⁡x)2exdx−∫exsin⁡x+1dx+C =excos⁡x1+sin⁡x+∫11+sin⁡xexdx−∫ex1+sin⁡xdx+C=excos⁡x1+sin⁡x+C