Question

Prove that
$\int e^x({\tan }^{-1}x+\frac{1}{1+x^2})dx$

Answer 1

Using $\int \left(f\right(x)+f^{\prime }(x)e^{x}dx=f(x)$

where $f\left(x\right)={\tan }^{-1}x$

we get,

$\int e^x({\tan }^{-1}x+\frac{1}{1+x^2})dx=e^x{\tan }^{-1}x+c$