∫dxsin⁡x−cos⁡x+2 is equal to

∫dxsin⁡x−cos⁡x+2=∫dxsin⁡x22−cos⁡x22+2=∫dx2sin⁡xsin⁡π4−cos⁡xcos⁡π4+1=12∫dx1−cos⁡x+π4=12∫dx1−cos⁡2x2+π8=12∫dx2sin2⁡x2+π8=122∫cosec2⁡x2+π8dx=−122⋅−cot⁡x2+π812+C=12cot⁡x2+π8+C