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int ((x+2)/(x+4))^2 e^x dx is equal to...

`int ((x+2)/(x+4))^2 e^x dx` is equal to

A

`e^(x)((x)/(x+4))+c`

B

`e^(x)((x+2)/(x+4))+c`

C

`e^(x)((x-2)/(x+4))+c`

D

`((2x e^(2))/(x+4))+c`

Text Solution

Verified by Experts

The correct Answer is:
A
`I=int((x+2)/(x+4))^(2)e^(x) dx=int e^(x)[(x^(2)+4x+4)/((x+4)^(2))]dx`
`=int e^(x)[(x(x+4))/((x+4)^(2))+(4)/((x+4)^(2))]dx`
`=int e^(x)[(x)/(x+4)+(4)/((x+4)^(2))]dx`
`=e^(x) ((x)/(x+4))+C`
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