Find the integral of y=6/(e^x+2) using calculus.

First, use the substitution u=e^x (which implies dx=du/u) to make the integral ∫6/(u*(u+2)))du. Next seperate the fraction using partial fractions and expand to form 3∫1/u du - 3∫1/(u+2) du. Next integrate to get 3lnu - 3ln(u+2) + C. Finally, don't forget the "+ C"!

Answered by Jonathan P. Maths tutor

4340 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

If given two parametric equations for a curve, how would you work out an equation for the gradient?


Show by induction that sum_n(r*3^(r-1))=1/4+(3^n/4)*(2n-1) for n>0


You have a five-litres jug, a three-litres jug, and unlimited supply of water. How would you come up with exactly four litres of water (with no measuring cup)?


Using the substitution of u=6x+5 find the value of the area under the curve f(x)=(2x-3)(6x+%)^1/2 bounded between x=1 and x=1/2 to 4 decimal places.


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