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

5448 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

y(x) = x^2(1-x)e^-2x , find y'(x) in the form of g(x)e^-2x where g(x) is a cubic function to be found


The finite region S is bounded by the y-axis, the x-axis, the line with equation x = ln4 and the curve with equation y = ex + 2e–x , (x is greater than/equal to 0). The region S is rotated through 2pi radians about the x-axis. Use integration to find the


How do I find the equation of the normal to the curve y=x^2 at the point (x1,y1)? Where x1=2 and y1=4 .


Find f''(x), Given that f(x)=5x^3 - 6x^(4/3) + 2x - 3


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