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If intx^5e^(-4x^3)dx=(1)/(48)e^(-4x^3)(f...

If `intx^5e^(-4x^3)dx=(1)/(48)e^(-4x^3)(f(x))+c`, where c is contant of intergration then `f(x)` equals to (a) `-4x^3-1` (b) `-1-2x^3` (c) `4x^3+1` (d) `1-2x^3`

A

`-2x^(3)-1`

B

`4x^(3)+1`

C

`-2x^(3)+1`

D

`-4x^(3)-1`

Text Solution

Verified by Experts

The correct Answer is:
D
Let `-4x^(3)=t`
`-12 x^(2)dx=dt`
`therefore int x^(5)e^(-4x^(3))dx=(1)/(48) int t e^(t)=(1)/(48)e^(t) (t-1) =(1)/(48) e^(-4x^(3))(-4x^(3)-1)`
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