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int(e^((x^(2)+4lnx)-x^(3)e^(x^(2))))/(x-...

`int(e^((x^(2)+4lnx)-x^(3)e^(x^(2))))/(x-1)` dx equal to

A

`((e^(3lnx)-e^(lnx))/(2x))e^(x^(2))+C`

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
A
Let
`I=int(e^((x^(2)+4lnx))-x^(3)e^(x^(2)))/(x-1)dx=int(e^(x^(2)).x^(4)-x^(3)e^(x^(2)))/(x-1)dx`
`rArr I=intx^(3)e^(x^(2))dx=(1)/(2)intte^(t)dt,` where `t=x^(2)`
`rArr I=(1)/(2)(t-1)e^(t)+C=(1)/(2)(x^(2)-1)e^(x^(2))+C`
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