Question

Evaluate: $\int \frac{e^x(1+x)dx}{{\sin }^2\left(x{e}^x\right)}$

• A. $\cot \left(x{e}^x\right)$
• B. $-\cot \left(x{e}^x\right)$
• C. $-\tan \left(x{e}^x\right)$
• D. $-\cot \left(e^x\right)$

Answer 1

Answer: (B)

$-\cot \left(x{e}^x\right)$

Substitute $x{e}^x=t$
$\therefore (1.e^x+x.e^x)dx=dt$
Thus, $I=\int co{\sec }^{2}tdt=-\cot t+c=-\cot \left(x{e}^x\right)+c.$