Question

The value of $\int \frac{x{e}^{x}dx}{(1+x{)}^2}$ is equal to

• A. $e^x(1+x)+c$
• B. $e^x\left(1+x^2\right)+c$
• C. $e^x(1+x{)}^2+c$
• D. $\frac{e^x}{1+x}+c$

Answer 1

Answer: (D)

$\int \frac{(x+1-1)e^x}{(1+x{)}^2}dx$
$=\int e^x\left(\frac{1}{1+x}-\frac{1}{(1+x{)}^2}\right)dx$
$=\frac{e^x}{1+x}+c$