Question

$\int \frac{1+tanx}{e^x-cosx}dx$ is equal to

• A. $e^{-x}tanx+c$
• B. $e^{-x}x+C$
• C. $e^{x}secx+C$
• D. $e^{x}tanx+C$

Answer 1

Answer: (C)

Let $I=\int \frac{1+\tan x}{e^{-x}\cos x}dx$
$=\int e^x\sec xdx+\int e^x\sec x\tan xdx$
$=e^x\sec x-\int e^x\sec x\tan xdx$
$+\int e^x\sec x\tan xdx+c$
$=e^x\sec x+c$