How to show steps of Integrate[Exp[-(I*(s*t))]/(Sqrt[2*Pi]*Sqrt[s]), {s, 0, Infinity}]? [duplicate]

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Get a “step-by-step” evaluation in Mathematica

5 answers

I am trying to use Wolfram Alpha in Mathematica 10.2 to show me the steps for calculating the integral in the title, i.e I have written the following command:

show steps of Integrate[Exp[-(I*(s*t))]/(Sqrt[2*Pi]*Sqrt[s]), {s, 0, Infinity}]

in the Wolfram alpha command line, but it doesn’t show me the steps, can anyone help me on how to make Mathematica show me the steps for calculating this integral?

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1 Answer
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Rubi integration package by Albert Rich, shows the steps, using its rules, for indefinite integration.

I’ve used this to show the steps for each of the over 51,000 integrals in Albert’s independent integration test suite.

Here is how you’d do the above for this example

After you load the package, then type

stepInt[Exp[-(I*(s*t))]/(Sqrt[2*Pi]*Sqrt[s]), s]

It will now show that it used 3 rules to get to the final result

The stepInt is thanks to Albert. Here it is. It will continue printing each step until it reaches the final result, or until it determines it can’t solve it.

stepInt[u_, x_Symbol] :=
Block[{ShowSteps = True}, FixedPoint[Function[Print[#];
ReplaceAll[#, {Defer[Int] -> Int, Defer[Dist] -> Dist,
Defer[Subst] -> Subst}]], Int[u, x]];
Null]