Learning to Solve Equations of Motion with fxns dx/Sqrt[E-U(x)]

[nolanp2]

i'm learning how to integrate equations of motion but can't get very far solving anything because i can't figure out how to integrate fxns of the type dx/Sqrt[E-U(x)] . The only solutions my lecturer gives me to these questions are using mathematica but i need to do them in tests so i need to find a method. can anyone help me out?

 

[Dick]

Depends very much on the form of U(x).

 

[nolanp2]

U(x) = A[1-e^(-ax)] is there a trick to solving this?

 

[HallsofIvy]

It would seem obvious to me to try the substitution u= 1- e^-ax.
Of course, you would then know that e^-ax= 1- u.