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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

`((2xe^(x))/(x+4))+C`

Text Solution

Verified by Experts

The correct Answer is:
A
Let `l=int((x+2)/(x+4))^(2)e^(x)dx=inte^(x)[(x^(2)+4+4x)/((x+4)^(2))]dx`
`rArr" "l=int e^(x)[(x(x+4))/((x+4)^(2))+(4)/((x+4)^(2))]dx`
`rArr" "l=int (e^(x)x)/(x+4)dx+int(4e^(x))/((x+4)^(2))dx`
On using integration by parts, we get
`rArr" "l=e^(x)((x)/(x+4))-int(4e^(x))/((x+4)^(2))dx+int(4e^(x))/((x+4)^(2))dx`
`rArr" "l=(xe^(x))/((x+4))+C`
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