Evaluate intsqrt(cotx)dx....

Evaluate `intsqrt(cotx)dx`.

A

`(1)/(sqrt(2))tan^(-1)((cotx-1)/(sqrt(2cotx)))-(1)/(2sqrt(2))log|(1+cotx-sqrt(2cotx))/(1+cotx+sqrt(2cotx))|+c`

B

`(-1)/(sqrt(2))tan^(-1)((cotx-1)/(sqrt(2cotx)))+(1)/(2sqrt(2))log|(1+cotx-sqrt(2cotx))/(1+cotx+sqrt(2cotx))|+c`

C

`(-1)/(sqrt(2))tan^(-1)((cotx-1)/(sqrt(2cotx)))+(1)/(2sqrt(2))log|(1+cotx-sqrt(2cotx))/(1+cotx+sqrt(2cotx))|+c`

D

`(1)/(sqrt(2))tan^(-1)((cotx-1)/(sqrt(2cotx)))+(1)/(2sqrt(2))log|(1+cotx-sqrt(2cotx))/(1+cotx+sqrt(2cotx))|+c`

Text Solution

Verified by Experts

The correct Answer is:

C

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