Question

integral of 1/e power x +1

Answer 1

To solve Integral  1/[eˣ + 1)  dx

Partial fraction method after substituting y = e^x.

$Let \: e^x = y, \: so \: e^x \: dx=dy \: or \: dx=\frac{dy}{y}\\\\I= \int {\frac{1}{e^x +1}} \: dx\\\\=\int {\frac{1}{y (y+1)}} \, dy \\\\Use \: Partial \: Fractions\\\\ I= \int {(\frac{1}{y}-\frac{1}{y+1})} \, dy\\\\ = Ln \frac{y}{y+1}+K\\\\ = Ln \: \frac{1}{1+e^{-x}} + K$

Answer is  - Ln (1+e⁻ˣ) + K