Question

$\int e^{log(1+ta{n}^{2}x)}dx$ on $I\subset R[\frac{(2n+1)\pi }{2}:nϵZ]$

Answer 1

$\int e^{log}(1+{\tan }^{2}x)dx$

$=\int (1+{\tan }^{2}x)dx\to [e^{{\log }^x}=x]$

$=\int {\sec }^{2}xdx$

$=\tan x\to [\int {\sec }^{2}xdx=\tan x]$