Question

Evaluate $\int e^x\sec x(1+\tan x)dx$.

Answer 1

$\int e^x\sec x(1+\tan x)dx$

$\Rightarrow \int e^x[\sec x+\sec x+\tan x]dx$

using $\int e^x\left(f_{1}x\right)+f^1\left(x\right)dx=e^{x}f\left(x\right)$

so, $\Rightarrow e^x\sec x$