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int sqrt(cos 2x)/(sin x) dx =...

`int sqrt(cos 2x)/(sin x) dx =`

A

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

B

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

C

`1/(4 sqrt(2)) log |(sqrt(2)-sqrt(1-tan^(2) x))/(sqrt(2)+sqrt(1-tan^(2)x))|+1/2 log |(1-sqrt(1-tan^(2) x))/(1+sqrt(1-tan^(2) x))+c`

D

`1/(4sqrt(2)) log |(2-sqrt(1-tan^(2) x))/(2+sqrt(1-tan^(2) x))|+1/(2sqrt(2)) log |(1-sqrt(1-tan^(2)x))/(1+sqrt(1-tan^(2) x))|+c`

Text Solution

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The correct Answer is:
B
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