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inte^(x^(4))(x+x^(3)+2x^(5))e^(x^(2))dx ...

`inte^(x^(4))(x+x^(3)+2x^(5))e^(x^(2))dx` is equal to

A

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

B

`(1)/(2)x^(2)e^(x^(4))+C`

C

`(1)/(2)e^(x^(2))e^(x^(4))+C`

D

`(1)/(2)x^(2)e^(x^(2))e^(x^(4))+C`

Text Solution

Verified by Experts

The correct Answer is:
d
Let `x^(2)=t` then ,
`I=e^(x^(4))(x+x^(3)+2x^(5))e^(x^(2))dx=(1)/(2)inte^(t^(2))(1+t+2t^(2))e^(t)dt`
`rArrI=(1)/(2)inte^(t){underset(f)(te^(t^(2)))+underset(f)((e^(t^(2))+2t^(2)e^(t^(2))))}dt`
`rArrI=(1)/(2)e^(t)(te^(t^(2)))+C=(1)/(2)x^(2)ex^(2)e^(x^(4))+C`
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