The function f whose graph passes through (0 ,0 )and whose derivative is cos4⁡x+sin4⁡xcos2⁡x−sin2⁡x is given by

We have f(x)=∫cos4⁡x+sin4⁡xcos2⁡x−sin2⁡xdxUsing, 2cos4⁡x+sin4⁡x=cos2⁡x+sin2⁡x2+cos2⁡x−sin2⁡x2, we can write  f(x)=12∫1cos2⁡x−sin2⁡xdx                               +12∫cos2⁡x−sin2⁡xdx=12∫sec⁡2xdx+12∫cos⁡2xdx=14log⁡tan⁡x+π4+14sin⁡2x+C=14log⁡1+tan⁡x1−tan⁡x+12sin⁡xcos⁡x+CSince f(0)=0 , we get C= 0.