Question

Solve
$\int \frac{1+x^{-1}}{1+x}dx$

Answer 1

Given,

$\int \frac{1+x^{-1}}{1+x}dx$

Let $f\left(x\right)=\frac{1+\frac{1}{x}}{1+x}$

$=\frac{\frac{x+1}{x}}{1+x}$

$=\frac{1}{x}$

$\to \int f\left(x\right)dx=\int \frac{1}{x}dx$

$=\log x+c$