Classical Mechanics: Linear movement against a constant force

[cemtu]

Homework Statement

A boat with initial velocity Vo starts to slow down by the resistive force F=-b(e^cv) (b and c are constants v is the velocity of the boat) by water when the engines are stopped.
a)Find the velocity v(t)
b)Find the time required for the boat to stop
c)Find the distance until the boat completely stop

Relevant Equations

$F = mdv/dt = -b(e^c)^v$

I solved this question until the end of the "c)Find the distance until the boat completely stop"
However I can not solve the integral I encounter in the solution of the last part of c).

Would you please check for math and maybe my mistakes and tell me what to do? Here:

 

[TSny]

Can you identify the mistake in this line?

 

[cemtu]

Awful sign and writing mistakes. :D
Thank you mister TSny! However, correcting these writing mistakes does not help me solve the integral at part c) of my question. :D

 

[haruspex]

Homework Statement:: A boat with initial velocity Vo starts to slow down by the resistive force F=-b(e^cv)

Are you sure this is a correct statement of the problem? Note what happens at v=0.
Is it perhaps a force $F=-b(e^{cv}-1)$ ? But that would make for a very nasty integral.

 

[haruspex]

solve the integral at part c)

I assume you now have an integral of the form $\int \ln(At+B).dt$. When faced with $\int f(t).dt$ which you don't know, a good place to start is tf(t). Differentiate that to see what you get and what adjustments you need to make.