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Question

Evaluate I=ex(1+sinx)+ex(1sinx)1+cosxdx
  1. (exex)tanx2+c
  2. (exex)cosecx2+c
  3. (exex)cotx2+c
  4. (exex)secx2+c


Solution

The correct option is D (exex)secx2+c
I=ex(1+sinx)+ex(1sinx)1+cosxdx
We know that
ex(f(x)+f(x))dx=exf(x)+c
I=exex+(exex)sinx1+cosxdxI=[ex+ex2sec2x2+(exex)tanx2]dx
I=12[ex(sec2x2+2tanx2)dx+ex(sec2x22tanx2)dx]
I=(exex)tanx2+c
 

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