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

5511 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Use the Chain Rule to differentiate the following equation: y=e^(3-2x)


The polynomial p(x) is given by p(x) = x^3 – 5x^2 – 8x + 48 (a) (i) Use the Factor Theorem to show that x + 3 is a factor of p(x). [2 marks] (ii) Express p(x) as a product of three linear factors. [3 marks]


Find the derivative, dy/dx, of y = 8xcos(3x).


Differentiate tan^2(x) with respect to x


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