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int e^(tan^(-1)x)/(1+x^(2))[(sec^(-1) sq...

`int e^(tan^(-1)x)/(1+x^(2))[(sec^(-1) sqrt(1+x^(2)))^(2)+ cos^(-1) ((1-x^(2))/(1+x^(2)))]dx, x gt 0`

A

`e^(tan^(-1)x. tan^(-1)x`

B

`1/2 e^(tan^(-1)x(tan^(-1)x)^(2)`

C

`e^(tan^(-1)x) (sec^(-1)sqrt(1+x^(2)))^(2)`

D

`e^(tan^(-1)x) (cosec^(-1)sqrt(1+x^(2)))^(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
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