Question

The value of the integeral $\underset{-1}{\overset{1}{\int }}$$\left\{\frac{x^{2015}}{e^{|x|}\left(x^2+cosx\right)}+\frac{1}{e^{|x|}}\right\}$ dx is equal to

• A. 0
• B. $1-e^{-1}$
• C. $2e^{-1}$
• D. $2\left(1-e^{-1}\right)$

Answer 1

Answer: (D)

$\Rightarrow \underset{-1}{\overset{1}{\int }}\left(odd+\frac{1}{e^{|x|}}\right)dx$
$=0+2\underset{0}{\overset{1}{\int }}\frac{dx}{e^x}=2\left(1-e^{-1}\right)$