∫sin3xdxcos4x+3cos2x+1tan−1secx+cosx
logTan−1Secx+Cosx+C
logCot−1Cosex+Cotx+C
logTan−1Secx−Tanx+C
logCot−1Cosex−Cotx+C
I=∫sin3xdxcos4x+3cos2x+1tan−1(secx+cosx) Put tan−1(secx+cosx)=t or 11+(secx+cosx)2(secxtanx−sinx)dx=dt or cos2xcos2x+1+cos2x2sinx1cos2x−1dx=dt
or cos2xsinx1−cos2xcos2xcos2x+1+cos4x+2cos2xdx=dtor sin3xcos4x+3+cos2x+1dx=dtI=∫dtt=log|t|+c =logtan−1(secx+cosx)+c