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## Homework Statement

v(dv/dx)= k(2v+1)

Find an explicit solution for x in terms of v.

## Homework Equations

v=speed, x=distance, k=constant

## The Attempt at a Solution

I can solve this by dividing by (2v+1), then integrating with respect to x using the chain rule.

I believe there is another method, though, involving substitution of 2v+1=u

so:

v(dv/dx)= ku

Now I'm not sure how (or even if it's possible) to integrate ku with respect to x, as it is a function of v, not x. Can someone point me in the right direction?