Question

Question #ea2e9

Answer 1

`int (2x)/e^x dx = -2e^(-x)(x+1)+C`

Explanation:

Considering that `1/e^x = e^(-x)` we can write the integral as:

`int (2x)/e^x dx = 2int xe^(-x)dx`

and integrate by parts:

`int (2x)/e^x dx = -2int xd(e^(-x)) = -2xe^(-x) +2inte^(-x)dx`

`int (2x)/e^x dx = -2xe^(-x) -2e^(-x) +C`

`int (2x)/e^x dx = -2e^(-x)(x+1)+C`