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

4672 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Calculate dy/dx of the following equation: y = 3x^3 - 6x^2 + 2x - 6


Differentiate with respect to x. y(x) = e^(7x^2)


A 10 kilogram block slides down a 30 degree inclined slope, the slope has a coefficient of friction of 0.2. Calculcate the blocks acceleration down the slope.


how to find flight time/distance and greatest hight of projectiles?


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences