Question

$\int e^{\sin x}(x \cos x-\sec x \tan x) d x=$ _____$+C;0 < x < \frac{\pi}{2} $.

• A. $e^{\sin x}(x-\sec x)$
• B. $e^{\sin x}(\sec x-x)$
• C. $e^{\sin x} x \cos x$
• D. $e^{\sin x}(x+\sec x)$

Answer 1

Answer: (A)

$\int xe ^{\sin x} \cos x-\int e^{\sin x} d x-\left[\left(\sec x \cdot e^{\sin x}\right)-\int e^{\sin x} d x\right]$
$e^{\sin x}(x-\sec x)+C$