∫sin4⁡xcos2⁡xdx is equal to

I=∫sin4⁡xcos2⁡xdx=∫sec2⁡x1−cos2⁡x2dx=∫sec2⁡x1+cos4⁡x−2cos2⁡xdx=∫sec2⁡x+cos2⁡x−2dx=∫sec2⁡x+1+cos⁡2x2−2dx=∫−32+12cos⁡2x+sec2⁡xdx=−32x+14sin⁡2x+tan⁡x+C