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intx.tan^-1xdx...

`intx.tan^-1xdx`

A

`(1)/(2)(x^(2)+1)tan^(-1)x-(1)/(2)x+C`

B

`(1)/(2)(x^(2)-1)tan^(-1)x-(1)/(2)x+C`

C

`(1)/(2)(x^(2)+1)tan^(-1)x+(1)/(2)x+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`I=intunderset(II)(x)underset(I)(tan^(-1))xdx=(tan^(-1)x)*(x^(2))/(2)-(1)/((1+x^(2)))*(x^(2))/(2)dx`
`=(1)/(2)x^(2)(tan^(-1))-(1)/(2)int(1-(1)/(1+x^(2)))dx=(1)/(2)x^(2)tan^(-1)x-(1)/(2)x+(1)/(2)tan^(-1)x+C`
`=(1)/(2)(x^(2)+1)tan^(-1)x-(1)/(2)x+C`
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