Let `A=int_(0)^(1)(e^(x))/(x+1)` dx then answer the following questions in terms of A.
Q. `int_(0)^(1)((x)/(x+1))^(2)e^(x)dx` equals

Options

A. `A-(e)/(2)`
B. `(e)/(2)+1-A`
C. `(e)/(2)+1-A`
D. `(e)/(2)-A`

Answer

C

Explanation

`int_(0)^(1)((x)/(x+1))^(2)e^(x)dx=int_(0)^(1)(((x+1)^(2)-(2x+1))/((x+1)^(2))).e^(x)dx`
`I=int_(0)^(1)e^(x)dx-2int_(0)^(1)(e^(x))/(x+1)dx+int_(0)^(1)(1)/((x+1)^(2))e^(x)dx`
`I=(e-1)-2A+(-(e)/(2)+1+A)=(e)/(2)-A`