Question

\int e^{x} \left\\{\frac{1+\sin x \cos x}{\cos^{2} x}\right\\} dx =

• A. $e^x \cos x +c$
• B. $e^x \sec x \, \tan x +c$
• C. $e^x \tan x +c$
• D. $e^x \cos^2 x - 1 + c$

Answer 1

Answer: (C)

$e^x \tan x +c$

Answer 2

$\int e^{x} \left(\frac{1+\sin x \cos x}{\cos^{2} x}\right) dx$
$= \int e^{x}\left(\sec^{2} x + \tan x\right)dx$
$= \int e^{x} \sec^{2} x dx +\int e^{x}\tan x dx$
$=e^{x} \tan x+c$