A) \[2\tan x+c\]
B) \[\sqrt{\cot x}+c\]
C) \[2\sqrt{\tan x}+c\]
D) \[{{\tan }^{2}}x+c\]
E) \[\cot x+c\]
Correct Answer: C
Solution :
Let \[I=\int{\frac{\sqrt{\tan x}}{\sin x\cos x}}dx\] \[=\int{\frac{\sqrt{\tan x}}{\tan x}}{{\sec }^{2}}x\,dx\] \[=\int{\frac{1}{\sqrt{\tan x}}.}{{\sec }^{2}}x\,dx\] \[=\frac{\sqrt{\tan x}}{1/2}=2\sqrt{\tan x}+c\]
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