Question

Evaluate : $\int \frac{e^x+1}{e^x+x}\cdot dx$

Answer 1

Let $t=e^x+x$

$\Rightarrow dt=e^x+1.dx$

$\int \frac{dt}{t}=\ln t+c$ where $c$ is the constant of integration.

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