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### Evaluate the indefinite integral

I am trying to solve the indefinite integral with user-defined rules. the integral expression and details are shown below where the P is a function of a,b and c. and I would like Mathematica to ...
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### How to get details about how Mathematica did a definite Integral

Assuming[{Element[S, Reals],S>0},Integrate[Exp[-I*S*w]/(w^2 + 1)^(3/2) ,{w, 0, Infinity}]] gets ...
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### Where can I find examples of good Mathematica programming practice?

I consider myself a pretty good Mathematica programmer, but I'm always looking out for ways to either improve my way of doing things in Mathematica, or to see if there's something nifty that I haven't ...
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### Can Wolfram Development platform use wolfram alpha?

I would like to be able to acces/show the step by step solutions from wolfram alpha in a note book! Is this possible? An
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### How does Mathematica calculate integrals? [duplicate]

One can use mathematica to get $$\int_{-\infty}^{\infty}\frac{\sin^2x}{x^2+1}\ dx=\frac{\pi \sinh 1}{e}.$$ Here are my questions: [Edited:] Is there a way that I can see the intermediate steps ...
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### functional derivative a functional

Can we calculate step by step functional derivative of the following functional by Mathematica? $$J(y) = \int_{x_0}^{x_1} \left( y^6(x) \right) \, \mathrm{d}x$$
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### Equivalent of Maple ShowSolution command in *Matematica* [duplicate]

While responding to a comment (...solve it by hand quickly) on this question, I used Maple to see all the steps in an integration, differentiation, and limit, like this The Maple command ...
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I am calling ...