Question

$\int{\frac{\sec x cosec x}{2\cot x-\sec x\cos ecx}}dx$ is equal to

• A. $\log |\sec x+\tan x|+c$
• B. $\log |\sec x+\cos ecx|+c$
• C. $\frac{1}{2}\log |\sec 2x+\tan 2x|+c$
• D. $\log |\sec 2x+\cos ec2x|+c$

Answer 1

Answer: (C)

$\frac{1}{2}\log |\sec 2x+\tan 2x|+c$

Answer 2

$\int{\frac{\sec x\cos ecx}{2\cot x-\sec x\cos ecx}}dx$
$=\int{\frac{\frac{1}{\cos x\sin x}}{\frac{2\cos x}{\sin x}-\frac{1}{\sin x\cos x}}}dx$
$=\int{\frac{dx}{2{{\cos }^{2}}x-1}}$
$=\int{\frac{dx}{{{\cos }^{2}}x-{{\sin }^{2}}x}=\int{\sec 2x\,dx}}$
$=\frac{1}{2}\log |\sec 2x+\tan 2x|+c$