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)

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