Question

$\int e^x \sin e^{x-1} d x$ is equal to

• A. $-\cos e ^{ x -1}+ C$
• B. $- e \cos e ^{ x -1}+ C$
• C. $\cos e ^{ x -1}+ C$
• D. $-\frac{1}{ e } \cos e ^{ x -1}+ C$

Answer 1

Answer: (B)

$ I=\int e^x \sin \left(e^x \cdot e^{-1}\right) d x \text { let } e^{x-1}=t ; e^{x-1} d x=d t $
$\int e \sin t d t=-e \cos t+C=-e \cos e^{x-1}+C$