int sqrt(1+ cosec)xdx equals-...

`int sqrt(1+ cosec)xdx` equals-

`2 sin^(-1) sqrt(sin x)+c`

`sqrt(2) cos^(-1) sqrt(cos x)+c`

`c-2 sin^(-1) (1-2 sin x)`

`sin^(-1)(2 sin x-1)+c`

Verified by Experts

The correct Answer is:

A, D

METHOD OF SUBSTITUTION
CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (Integer Answer Type)|5 Videos
METHOD OF SUBSTITUTION
CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (Matrix Match Type)|2 Videos
METHOD OF SUBSTITUTION
CHHAYA PUBLICATION|Exercise EXERCISE 6B (Long Answer Type Questions)|28 Videos
MEASURMENT OF TRIGONOMETRICAL ANGLES
CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams (Assertion -Reason Type)|2 Videos
MISCELLANEOUS EXAMPLES
CHHAYA PUBLICATION|Exercise WBJEE 2026|23 Videos

int cosec x dx is equal to-

`cosec x cot x+c`

`log | tan ""(x)/(2)|+c`

`log | cot ""(x)/(2)|+c`

`cosec x - cot^(2) x+c`

`2 log abs (cos x/2 + sqrt(cos^2 x/2 - 1/2))` + c

`log abs (cos x/2 + sqrt(cos^2 x/2 - 1/2))` + c

`-2 log abs (cos x/2 + sqrt(cos^2 x/2 - 1/2))` + c

None of these

`2[sqrt(e^(x)-1)+tan^(-1) sqrt(e^(x)-1)]+c`

`sqrt(e^(x)-1)-tan^(-1) sqrt(e^(x)-1)+c`

`sqrt(e^(x)-1)+tan^(-1)sqrt(e^(x)-1)+c`

`2[sqrt(e^(x)-1)-tan^(-1) sqrt(e^(x)-1)]+c`