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int(e^(x)(x-2))/(x(x^(2)+e^(x)))dx AAx g...

`int(e^(x)(x-2))/(x(x^(2)+e^(x)))dx AAx gt0` is equal to

A

`ln(1+(e^(x))/(x^(2)))+c`

B

`ln(-(1)/(2)+(e^(x))/(x^(2)))+c`

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
A
`int(e^(x)(x-2))/(x(x^(2)+e^(x)))dx=int(3x^(2)+e^(x)+xe^(x)-3x^(2)-3e^(x))/(x(x^(2)+e^(x)))dx`
`=int(d(x^(3)+xe^(x)))/(x^(3)+xe^(x))-3int(dx)/(x)`
`=ln(x^(3)+xe^(x))-3ln x+c`
`=ln((x^(2)+e^(x))/(x^(2)))+c=ln(1+(e^(x))/(x^(2)))+c`
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