I need to integrate this function once with respect to t to find an expression for h(t):

v(t) = -k ln(m-bt) - gt + k ln(m)

Can anyone show me how to do this? How would I resolve the constant?

I then need to show that, after substituting t into h(t) I get the expression:

h(t) = km/b [(1 - X) ln(1 - X) + X(1 - (g/2kb)Xm0)]

Sorry I wasn't sure how to put that into LaTeX, I hope it's clear enough in that form.

I should mention also that k, b, m and g are constants. This is all to find an expression for h(t) when the rocket reaches the end of its boost phase. Thanks.