Question

$\int e^x(\frac{2\tan x}{1+x}+{\tan }^2(x+\frac{\pi }{4}))dx$ is equal to

• A. $e^x\tan (\frac{\pi }{4}-x)+c$
• B. $e^x\tan (x-\frac{\pi }{4})+c$
• C. $e^x\tan (\frac{3\pi }{4}-x)+c$
• D. none of these

Answer 1

The correct option is B $e^x\tan (x-\frac{\pi }{4})+c$

$\int e^x(\frac{2\tan x}{1+\tan x}+{\tan }^2(x-\frac{\pi }{4}))dx$
$\int e^x(\tan (x-\frac{\pi }{4})+{\sec }^2(x-\frac{\pi }{4}))dx$
$=e^x\tan (x-\frac{\pi }{4})+C$
Ans: B