What's the principle of Wolfram's function "Integrate"

Question

It says"Wolfram uses standard principle to calculate integration"

What does it mean?

Answer 1

Presumably it means standard algorithmic methods. (No special magic.)

https://reference.wolfram.com/language/tutorial/Integration.html

"The Wolfram Language knows how to do almost any integral that can be done in terms of standard mathematical functions."

The following information is from a paper relating to symbolic integration in Mathematica 5 and 6. (The current version is Mathematica 11.)

http://library.wolfram.com/infocenter/Conferences/5832/DefiniteIntegration.pdf

Indefinite Integration

The indefinite integration code consists primarily of a partial implementation of the Risch algorithm [2, 5], in addition to extensive table lookup methods. …

Definite Integration

Definite integration is done via a number of methods as indicated below.

• Special case contour integration.
• Newton−Leibniz code specialized for integrands of the form rational x trig or rational x exponential.
• Newton−Leibniz code specialized for integrands containing logs or polylogs.
• A general case implementation of Newton−Leibniz integration.
• An implementation of definite integration by convolution of MeijerG functions [1].

Mathematica also performs numerical integration.

https://reference.wolfram.com/language/tutorial/NIntegrateIntegrationStrategies.html