I'm having trouble on a question in my calculus project about "Landing an airliner". It is not very complex and I understand everything but this problem.

They even give me the solution to the problem, just need to figure out how they got there.

"Integrate the relation u(t)=dx/dt and use the condition x(0)=-L to show that,

"

Shown below is what I'm trying to integrate to get x(t), which is shown above.

I'm in a loop here people , any help would be greatly, greatly appreciated.