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int(x-3)/((x-1)^(3)).e^(x)dx is equal to...

`int(x-3)/((x-1)^(3)).e^(x)dx` is equal to

A

`(e^(x))/((x-1))+C`

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
D
Let `l=int(x-3)/((x-1)^(3))e^(x)dx=int(x-1-2)/((x-1)^(3))e^(x)dx`
`=inte^(x)[(x-1)/((x-1)^(3))-(2)/((x-1)^(3))]dx`
`=inte^(x)[(1)/((x-1)^(2))-(2)/((x-1)^(3))]dx`
Let `f(x)=(1)/((x-1)^(2)) rArr f'(x)=(-2)/((x-1)^(3))`
`therefore" "l=(e^(x))/((x-1)^(2))+C`
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