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

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

A

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

B

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

C

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

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
d
Let `I=int(e^(x^(x)+4Inx)-x^(3)e^(x^(2)))/(x-1)dx=int(e^(x^(2)).x^(4)-x^(3)e^(x^(2)))/(x-1)dx`
`rArrI=intx^(3)e^(x^(2))dx=(1)/(2)intte^(t)dt`, where `t=x^(2)`
`I=(1)/(2)(t-1)e^(t)+C=(1)/(2)(x^(2)-1)e^(x^(2))+C`
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OBJECTIVE RD SHARMA-INDEFINITE INTEGRALS-Solved Example
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