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

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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
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Correct Answer - 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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