Integral Calculus Question 284
Question: $ \int_{{}}^{{}}{\frac{\cos 2x+2{{\sin }^{2}}x}{{{\cos }^{2}}x}dx=} $
Options:
A) $ 2\sec x+c $
B) $ 2\tan x+c $
C) $ \tan x+c $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ \int_{{}}^{{}}{\frac{\cos 2x+2{{\sin }^{2}}x}{{{\cos }^{2}}x},dx}=\int_{{}}^{{}}{\frac{2({{\cos }^{2}}x+{{\sin }^{2}}x)-1}{{{\cos }^{2}}x},dx} $ $ =\int_{{}}^{{}}{{{\sec }^{2}}x,dx}=\tan x+c $ .
BETA
