If you have to integrate:
If you say, let , you'll get:
Try to split up in partial fractions:
Determine A and B.
I am trying to integrate the following expression:
(where "u" is it should read " " but I couldn't get the LaTex maths thing to work, sorry)
using the given substitution
Please can anyone offer a way to do this? I get to the stage where I have:
(where "a" is it should read "u(u-4)")
but I can't get any further. Any help would be much appreciated.
I get the right answer (or at least the same answer as the book) when I use
I also get the right answer when I use the substitution v = 4u - 16.
So thanks to e^(i*pi) and HallsofIvy.
As for using the substitution and Plato's answer, I have no idea what's going on!!
Multiply the numerator and denominator of your integrand by e^(-2x) to get what Plato has. Then make the substitution u = 1 + 4e^(-2x) and the answer is immediate. ln|1 + 4 e^(-2x)| and ln|e^(2x) + 4)|-2x are equivalent by the way ...... (Use basic log rules to prove this).