Basic methods: linear integration, substitution integration and integration by parts. Common skills: differential integration, variable substitution, trigonometric function substitution, radical substitution, inverse substitution, direct substitution of complex variable function, trigonometric substitution after constant deformation, partial integration, rational function integration and paired integration.

The specific introduction of integral:

Integral is the core concept in calculus and mathematical analysis. Usually divided into definite integral and indefinite integral. Intuitively speaking, for a given positive real function, the definite integral in the real number interval can be understood as the area value (a definite real value) of the curve trapezoid surrounded by curves, lines and axes on the coordinate plane.

Bernhard Riemann gave a strict mathematical definition of integral (see "Riemann integral"). Riemann's definition uses the concept of limit, imagining a curved trapezoid as the limit of a series of rectangular combinations. Since the19th century, with the integration of various types of functions in various integration fields, a more advanced definition of integration has gradually emerged.

For example, path integral is the integral of multivariate function, and the interval of integral is no longer a line segment (interval [a, b]), but a curve segment on the plane or in space; In area integration, curves are replaced by surfaces in three-dimensional space. Integral in differential form is a basic concept in differential geometry.

Basic introduction:

The driving force of overall development comes from the demand in practical application. In practice, some unknowns can sometimes be roughly estimated, but with the development of science and technology, it is often necessary to know the exact values. If the area or volume of simple geometry is needed, the known formula can be applied.

For example, the volume of a rectangular swimming pool can be calculated by length x width x height. But if the swimming pool is oval, parabolic or more irregular, it is necessary to calculate the volume by integral. In physics, it is often necessary to know the cumulative effect of one physical quantity (such as displacement) on another physical quantity (such as force), and integration is also needed at this time.