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Evaluate : (i) int(sinx)/(sqrt(4cos^...

Evaluate : (i) `int(sinx)/(sqrt(4cos^(2)x-1))dx`
(ii) `int(sec^(2)x)/(sqrt(tan^(2)x-4))dx`

A

`log|tanx-sqrt(tan^(2)x-4)|+C`

B

`log|tanx+sqrt(tan^(2)x-4)|+C`

C

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

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Put `tan x=t and sec^(2)xdx=dt . Then,`
`I=int(dt)/(sqrt(t^(2)-2^(2)))=log |t+sqrt(t^(2)-4)|+C=log|tanx+sqrt(tan^(2)x-4)|+C.`
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