The integral ∫cos⁡4x−1cot⁡x−tan⁡x is equal to

Put cos⁡2x=t Then −2sin⁡2xdx=dt and theintegral becomes∫−2sin2⁡2xcos2⁡x−sin2⁡xcos⁡xsin⁡xdx=−∫1−cos2⁡2xcos⁡2xsin⁡2xdx=12∫1−t2tdt=12log⁡|t|−t22+C=12log⁡|cos⁡2x|−14cos2⁡2x+C.