First of all, we should memorize the basic indefinite integral (corresponding derivative formula) and its properties (satisfying addition and number multiplication). Method of substitution is the most commonly used method, including the first method of substitution (suitable for integral method of substitution) and the second method of substitution (generally used in indefinite integral with roots), as well as integration by parts (generally used in the case of recursion with n). For special functions: (1) rational functions can be transformed into the sum of the simplest true fractions; (2) Rational trigonometric functions can be transformed into rational functions by universal transformation; And (3) the irrational number function generally adopts Euler transformation or trigonometric substitution, the main purpose of which is to transform the root sign on the denominator into a numerator (generally, x is replaced by 1/t) and make the irrational number.

In the transformation, we can simplify and decompose the term to make the integrand function closer to the familiar form. In trigonometric functions, we should make full use of 1 (1 = sin 2x+cos 2x) substitution, angle doubling formula, sum-difference product and sum-difference formula.

Just finished learning indefinite integral. I hope I can help you? ^_^