- #1

Deuterium2H

- 59

- 0

Unfortunately, while I can understand much of the complex analysis, I sometimes get hung up over the what I believe are rather elementary integrals which are never solved in a step by step fashion...but are just shown and then (with no explanation) given a solution. This can be a bit frustrating, especially if it has been years (decades) since one had advanced Calc, and has forgotten many of the common integral forms/solutions.

Anyways, I didn't even get through the damn Preface without encountering a problem.

We are given the following differential equation (integral):

ds = [ v

_{0}/ (1 + kv

_{0}t) ] dt

k is a Constant of proportionality, and v

_{0}is initial velocity, which obviously itself is a function of time.

The solution is given as:

s = ln[(1 + kv

_{0}t)

^{(1/k)}] + Z

How does one integrate the right side of the equation? I can get the sense that the solution will be a natural logarithm, due to the fact that we have a form INTEGRAL (dt/t).

Would someone be so kind as to break this down step by step for me. I am almost embarrassed to ask, but oh well. Thanks in advance!