Question

$\underset{0}{\overset{1}{\int }}\frac{x{e}^x}{(2+x{)}^3}dx$ is equal to

• A. $\frac{1}{27},e-\frac{1}{8}$
• B. $\frac{1}{9}\cdot e+\frac{1}{4}$
• C. $\frac{1}{27}\cdot c+\frac{1}{8}$
• D. $\frac{1}{9}\cdot e-\frac{1}{4}$

Answer 1

Answer: (D)

$\underset{0}{\overset{1}{\int }}{e}^x\left[\frac{1}{(x+2{)}^2}-\frac{2}{(x+2{)}^3}\right]dx$
$={\left[\frac{e^x}{(x+2{)}^2}\right]}_0^1=\frac{e}{9}-\frac{1}{4}$