Question

$\int e^x\sin e^{x-1}dx$ 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)

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