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intx^(2)cosxdx=?...

`intx^(2)cosxdx=?`

A

`x^(2)sinx+2xcosx-2sinx+C`

B

`2xcosx-xsinx+2sinx+C`

C

`x^(2)sinx-2xsinx+2sinx+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`I=intunderset(I)(x^(2))underset(II)(cos)xdx=x^(2)sinx-intunderset(I)(2x)underset(II)(sin)xdx`
`=(x^(2)sinx)-2[x(-cosx)-int(-cosx)dx]+C`
`=(x^(2)sinx)+2xcosx-2sinx+C`.
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