Q. $\int_{}^{}{\frac{\cos{2x + 2\sin^{2}x}}{\cos^{2}x}dx}$ is equal to
A) $2\sec{x + c}$
B) $2\tan{x + c}$
C) $\tan{x + c}$
D) None of these
Explanation
(c)
$\int_{}^{}{\frac{\cos{2x + 2\sin^{2}x}}{\cos^{2}x}dx}$
$= \int_{}^{}{\frac{2\left( \sin^{2}{x + \cos^{2}x} \right) - 1}{\cos^{2}x}dx}$
$= \int_{}^{}{\sec^{2}x}dx = \tan x + c$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.