ln-1-e-x-dx-

Question Number 101597 by Rio Michael last updated on 03/Jul/20

\int \ln (1 + e^{x}) d x = . .

Commented by Dwaipayan Shikari last updated on 03/Jul/20

\int (e^{x} - \frac{1}{2} e^{2 x} + \frac{1}{3} e^{3 x} - \frac{1}{4} e^{4 x} + \frac{1}{5} e^{5 x} - \frac{1}{6} e^{6 x} + \dots .) d x

e^{x} - \frac{e^{2 x}}{4} + \frac{e^{3 x}}{9} - \frac{e^{4 x}}{16} + \frac{e^{5 x}}{25} - \frac{e^{6 x}}{36} + \frac{e^{7 x}}{49} - \frac{e^{8 x}}{64} + \dots \dots .

It is approximate

Commented by floor(10²Eta[1]) last updated on 03/Jul/20

\underset{k = 1}{\sum^{\infty}} \frac{{(- 1)}^{k + 1} e^{kx}}{k^{2}} + C

Commented by Rio Michael last updated on 03/Jul/20

thank you sir