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If int f(x)dx=psi(x), then int x^5f(x^3)...

If `int f(x)dx=psi(x)`, then `int x^5f(x^3)dx`

A

`(1)/(3)x^(3){x^(3)phi(x^(3))-intx^(2)phi(x^(3))dx}+C`

B

`(1)/(3)x^(3)phi(x^(3))-3intx^(3)phi(x^(3))dx+C`

C

`(1)/(3)x^(3)phi(x^(3))-intx^(2)phi(x^(3))dx+C`

D

`(1)/(3){x^(3)phi(x^(3))-intx^(3)phi(x^(3))dx}+C`

Text Solution

Verified by Experts

The correct Answer is:
c
Let `x^(3)=t`. then , `d(x^(3))=3dtrArr3x^(2)dx=dt`
`thereforeintx^(5)f(x^(3))dx`
`=(1)/(3)intx^(3)f(x^(3))(3x^(2))dx`
`=(1)/(3)intunderset(I)(t)f(t)underset(II)dt`
`=(1)/(3){tphi(t)-intphi(t)dt}+C` " " `[becauseintf(t)dt=phi(t)]`
`=(1)/(3){x^(3)phi(x^(3))-3intphi(x^(3))x^(2)dx}+C`
`=(1)/(3)x^(3)phi(x^(3))-intx^(2)phi(x^(3))dx+C`
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