Name: Anonymous 2009-01-15 18:21
How would you integrate 1/(u^3+ u) ? The background is needing to solve the integral of tanh(x) two ways - The Hyperbolic substitution part is easy, by we are also told to replace tanh(x) with it's e^x equivalent of (exp(x) - exp(-x)) / (exp(x) + exp(-x)) , substitute u for e^x, and solve from there.
You end up with two integrals - u/(u^2 +1) , simple, and 1/(u^3 + u) , less simple. What route should I take from here? Am I missing some subtle clue?
You end up with two integrals - u/(u^2 +1) , simple, and 1/(u^3 + u) , less simple. What route should I take from here? Am I missing some subtle clue?