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)

$\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$