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# tricky integration

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1. So I'm trying to find the equation of motion of a particle under the potential U = A(exp(-2ax) - 2exp(-ax)). I use the fact that kinetic energy + potential energy = total energy and I dunno how to deal with the integral.. here:

2. (Original post by StarvingAutist)
So I'm trying to find the equation of motion of a particle under the potential U = A(exp(-2ax) - 2exp(-ax)). I use the fact that kinetic energy + potential energy = total energy and I dunno how to deal with the integral.. here:

Complete the square inside the square root, then make a trigonometric substitution, so you can use the standard
results for integrals of 1/sqrt(a^2-x^2), 1/sqrt(a^2+x^2), etc.

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