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)

CF
Answered by Cory F. Maths tutor

5128 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Finding the tangent of an equation using implicit differentiation


How to differentiate e^x . sin(x)


How can I demonstrate that (sin(T)+cos(T))(1-sin(T)cos(T))=(sin(T))^3+(cos(T))^3


Solve x^2 + x=12 by factorising


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2026 by IXL Learning