Find the integral of e^3x/(1+e^x) using the substitution of u=1+e^x

Differentiate U with respect to x to find dx in terms of du and substitute into the integral so that it is in terms of du, then using e^3x = (e^x)^3 and u = 1+e^x subsitute u in for x and simplify the integral to u-2+1/u du and integrate with respect to u. Then subsituting x back in for u.The final answer being (1+e^x)^2/2 - 2(1+e^x) + ln(1+e^x)