anybody has an idea about how to integrate this?

Question

v(t)= sqrt[ gm/k ] tanh[ (kg/m)t ]

Answer 1

If v is just a function of t and the other varibles are all constants, then this is just integrating something in the form of
∫ a tanh(bt) dt, where a = √(gm/k) and b=(kg/m). In this case you'd have:
∫ a tanh(bt) dt =
a ∫ tanh(bt) dt =
(a/b) ∫ tanh(bt) * b dt =
(a/b) ln(cosh(bt)) + C

Answer 2

This same question was asked earlier today... weird
Anyways, the answer was ln |cosh(sqrt(kg/m)t)| + C

http://answers.yahoo.com/question/index;_ylt=Ar6WuM66_2XuLT.5QW..J.Tsy6IX?qid=20070628093634AA0tHiT&show=7#profile-info-w30NDszGaa

Answer 3

Integrating that function with respect to t, you get:

m/(g*k) * sqrt[g*m/k] * log[cosh[k*g/m * t]]

Answer 4

ln|cosh[(kg/m)*t]|*sqrt[(m/k)^3*1/g]