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Evaluate: inttan^(-1)((3x-x^3)/(1-3x^2))...

Evaluate: `inttan^(-1)((3x-x^3)/(1-3x^2))\ dx`

A

`3xtan^(-1)x+(3)/(2)log(1+x^(2))+C`

B

`3xtan^(-1)x-(3)/(2)log(1+x^(2))+C`

C

`3xcos^(-1)x-(3)/(2)sqrt(1+x^(2))+C`

D

`3xsin^(-1)x+(3)/(2)sqrt(1+x^(2))+C`

Text Solution

Verified by Experts

The correct Answer is:
B
Put `x=tant andtdx=sec^(2)tdt`.
`I=inttan^(-1)(tan3t)sec^(2)tdt=3underset(I)(t)underset(II)(sec^(2))tdt`.
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