I have defined a function first and then I need to integrate something to find the time (it's theoretical mechanics). I think I don't have any syntax issues but what am I doing not the way I should?

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I've tried wrapping the expression in Evaluate, but it gives the same result.

In case somebody would like the code, here it is:

U[x_] := Subscript[U, 0]*Tan[α*x]^2

t = 
    Integrate[1/Sqrt[E - U[x_]] , 
       1/α*Log[(A - Sqrt[A*(A - Abs[E])]/Abs[E])], 
       1/α*Log[(A + Sqrt[A*(A - Abs[E])]/Abs[E])]}]

closed as off-topic by MarcoB, m_goldberg, LCarvalho, Itai Seggev, J. M. is away Aug 8 '17 at 17:40

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  • 1
    $\begingroup$ It may just be because Mathematica doesn't know a closed form for your integral. Also, do you mean to use E in your code as an arbitrary constant? E is the basis of natural logarithms in Mathematica. Don't use variables with uppercase names, especially single-letter ones, as you risk conflicts with built-ins like this one. $\endgroup$ – MarcoB Aug 2 '17 at 21:02
  • $\begingroup$ FWIW, Integrate[1/Sqrt[a - b Tan[x]^2], x] does return a proper (elementary!) closed form. $\endgroup$ – J. M. is away Aug 4 '17 at 5:36
  • $\begingroup$ I see two issues: one major and one I don't know. Your definition of the function U is recursive, since U appears on both sides. Change the one on the left to lower-case or something else. The other is that in your definition of t, U[t_] should be U[t]. Finally, why do you have Abs[E]? E is by definition a positive number. I believe that E is supposed to be energy, but E is reserved for the number $e$ in Mathematica. In general, don't use upper case letters or capitalized words for user-defined functions and symbols. $\endgroup$ – march Aug 8 '17 at 16:10

When you call U in the integration, you should just say U[x], not U[x_]. You inadvertently left in the underscore pattern marker (a.k.a. Blank).

  • $\begingroup$ I changed it o U(x) still docent show anything. $\endgroup$ – Jeremy Aug 2 '17 at 17:12
  • $\begingroup$ Yeah, sorry to hear that. It was definitely a problem, and at least partly answered your question "what am I doing not the way I should", but I'm afraid I can't help beyond that. $\endgroup$ – Joel Klein Aug 3 '17 at 18:02

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