Use the substitution u=1+e^x to find the Integral of e^(3x) / (1 + e^x)
ex=u-1 so e3x=(u-1)3 and du/dx = ex so rearranging gives dx=e-x du Substituting all that information in the integral we get Integral ( (u-1)3/ (u(u-1)) du ) which simplifies to Integral (u -2 +1/u).Integrating we get u2/2 -2u + ln u + C and substituting the original variable we get (1+ex)2/2 -2(1+ex) + ln (1+ex) + C
IP
