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Evaluate: int(e^tan^((-1)x))/((1+x^2))[(...

Evaluate: `int(e^tan^((-1)x))/((1+x^2))[(sec^(-1)sqrt(1+x^2)+cos^(-1)((1-x^2)/(1+x^2))]dx(x >0)dot`

A

`e^(tan^(-1)x)*tan^(-1)x+C`

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
C
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