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int(xtan^-1x)/(1+x^2)^(3/2)dx...

`int(xtan^-1x)/(1+x^2)^(3/2)dx`

A

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

B

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

C

`(xtan^(-1)x)/(sqrt(1+x^(2)))+(1)/(2)log|(x)/(sqrt(1+x^(2)))|+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Put x=tan t, so that dx `=sec^(2)tdtandt=tan^(-1)x`.
`:." "I=int(t(tant))/((1+tan^(2)t)^((3)/(2)))sec^(2)tdt=intunderset(I)(t)underset(II)(sin)tdt`.
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