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intsqrtx e^(sqrtx)dx is equal to...

`intsqrtx e^(sqrtx)dx` is equal to

A

`2sqrtx-e^(sqrtx)-4sqrt(xe^(sqrtx))+C`

B

`(2x-4sqrtx+4)e^(sqrtx)+C`

C

`(2x+4sqrtx+4)e^(sqrtx)+C`

D

`(1-4sqrtx)e^(sqrtx)+C`

Text Solution

Verified by Experts

The correct Answer is:
B
Let`" "l=intsqrt(x e^(sqrtx)dx`
Put`" "x=t^(2)" "rArr" "dx=2tdt`
Now, integration by parts, we get
`l=2int t^(2)e^(y)dt=2[t^(2)e^(t)-(2t)e^(t)+2e^(t)]+C`
`=(2x-4sqrtx+4)e^(sqrtx)+C`
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