,x. ec ,x 2 ,x - x , ec ,x dx is (Where c is integral constant) - Vidyadip

MCQ

$\int {\frac{{\sec \,x.\cos ec \,x}}{{2\cot \,x - \sec x\,\cos ec \,x}}dx} $ is (Where $c$ is integral constant)

✓
$\frac{1}{2}\ln \left| {\sec \,2x + \tan \,2x} \right| + c$
B
$\ln \left| {\sec \,x + \cos ec \,x} \right| + c$
C
$\ln \left| {\sec \,x + \tan \,x} \right| + c$
D
$\frac{1}{2}\ln \left| {\sec \,x + \cos ec \,x} \right| + c$

✓

Answer

Correct option: A.

$\frac{1}{2}\ln \left| {\sec \,2x + \tan \,2x} \right| + c$

a
$I = \int {\frac{{\sec x \cdot \cos ec\,x}}{{2\cot x - \sec x\cos ec\,x}}} dx = \int {\frac{{dx}}{{2{{\cos }^2}x - 1}}} $

$=\int(\sec 2 x) d x$

$I = \frac{{\ln |\sec 2x + \tan 2x|}}{2} + c$

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