F'(x) = f(x)

Pairs of functions that satisfy the derivative relationship

∫f(x)dx = F(x) C

C is the integral constant

The graph of F(x) is the accumulation of the area under the graph of f(x)

Can be regarded as the sum of infinitesimal rectangular bars under the f(x) graph

F(x) represents the cumulative area from a certain point to point x

The area under a specific interval can be found by integrating

The indefinite integral of the sum is equal to the sum of the indefinite integrals of the functions

The indefinite integral of a constant multiple is equal to the indefinite integral of a constant multiple of the original function.

First substitution method

Second substitution method

Integration using the derivative rule of products

A function whose numerator and denominator are both polynomials

Processing when the degree of numerator is higher than the degree of denominator

1 General method (universal substitution)

2 special methods (triangular deformation, substitution, division), several common substitution methods

Determine whether it is a basic point

Determine whether you need to exchange dollars or partial points

Simplify integrals by algebraic transformations

Simplify integrals by trigonometric transformations

Verify the derivative of the original function

Check the applicability of the integration constant C

cost and benefit analysis

demand and supply analysis

Integrals of simple polynomial functions

Integrals of basic trigonometric functions

Mixed integrals of complex polynomials and trigonometric functions

Integral of exponential and logarithmic functions

Application of integrals in practical problems

Integration strategy selection for complex functions