Question

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

• 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)

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