Question

The value of $\int$ $(x{e}^{lnsinx}-cosx)$ dx is equal to :

• A. -x cos x + C
• B. sin x - x cos x + C
• C. $-e^{lnx}cosx+C$
• D. sin x + x cos x + C

Answer 1

The correct option is A -x cos x + C

$\begin{array}{c}I=\int \left(x{e}^{\log \sin x}-\cos x\right)dx\\ =\int \left(x\sin x-\cos x\right)dx\\ =-x\cos x+\int \cos xdx-\int \cos xdx+C\\ =-x\cos x+C\end{array}$

Hence,

Option $A$ is correct answer.