Evaluate: intsqrt(tanx)dx =...

Evaluate: `intsqrt(tanx)dx =`

A

(a) `1/(2sqrt(2))tan^(-1)((x^(2)-1)/(sqrt(2)x))+1/(2sqrt(2))logabs((x^(2)-sqrt(2)+1)/(x^(2)+sqrt(2)x+1))+c`

B

(b) `1/(2sqrt(2))tan^(-1)((x^(2)-1)/(sqrt(2)x))+1/(sqrt(2))logabs((x^(2)-sqrt(2)+1)/(x^(2)+sqrt(2)x+1))+c`

C

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

D

(d) `1/sqrt(2)tan^(-1)((tanx-1)/sqrt(2tanx))+1/(2sqrt(2))logabs((tanx-sqrt(2tanx)+1)/(tanx+sqrt(2tanx)+1))+c`

Verified by Experts

The correct Answer is:

D

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