∫dxsin⁡x+cos⁡x is equal to

∫dxsin⁡x+cos⁡x=12∫dxsin⁡(π/4)sin⁡x+cos⁡(π/4)cos⁡x=12∫dxcos⁡(x−π/4)=12∫sec⁡(x−π/4)dx=12log⁡tan⁡π4+x2−π8+C=12log⁡tan⁡π8+x2+C