So here it goes.

t=?

s=10

v=2s+1

v=ds/dt

dt=(1/v)ds

t=Iteg[1/v]ds

t=1/2Ln(2s+1)

This is the way it was solved in the book (I might have memorized the integration of v wrong).

But I tried to solve it like this

t=?

s=10

v=2s+1

v=ds/dt

ds=v*dt

s=(2s+1)t

s/(2s+1)=t

The solutions are clearly different. I don't understend why. The only idea I got was that I cant integrate v by dt becouse t is not a veriable in v and v is therfore threted as a constent what changes the whole thing (is this true). But if there are any beter explanations I would be glad to hear them. Thanks.