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"!

JP

Related Maths A Level answers

All answers ▸

Simplify and solve for x. log(x+1)+log 5=2. Note, log is the natural log in this case


Given that z = sin(x)/cos(x), use the quoitent rule to show that dZ/dx = sec^2(x)


Using the equation cos(a+b) = cos(a)cos(b) - sin(a)sin(b) or otherwise, show that cos(2x) = 2cos^2(x) - 1.


A ball of mass m moves towards a ball of mass km with speed u. The coefficient of restitution is 0. What is the final velocity if the first ball after the collision.