Evaluate :∫ex[sinx+cosx]1-sin2xdx
excosecx+c
ex+cotx+c
exsecx+c
extanx+c
Explanation for the correct option
Finding ∫ex[sinx+cosx]1-sin2xdx
Solving the integral,
=∫ex[sinx+cosx](1–sin2x)dx=∫exsinx+cosxcos2xdx[ 1=cos2x+sin2x]=∫exsinxcos2x+cosxcos2xdx=∫ex(secx×tanx+secx)dx=[exsecx]+c∵∫exf(x)+f'(x)=exf(x)+c
Hence, the correct answer is Option (C)