Basis of the mathematical analysis is integrated notation. It is one of the most difficult sections of a course of the higher mathematics. All difficulty is that there is no uniform algorithm on which it would be possible to solve all integrals.
Instruction
1. Integration is an operation which is opposite to differentiation. Therefore if you want well to learn to integrate, then you at first need to learn to find derivatives from any functions. It is possible to learn it quickly enough. There is a special table of derivatives. With its help it is already possible to solve simple integrals. And there is also a table of the main uncertain integrals. It is submitted in the drawing.
2. Now it is necessary to remember the the main properties of integrals given below.
3. It is the best of all to display integral from the sum of functions for the sum of integrals. This rule is most often applied when the composed functions rather simple if they can be found by means of the table of integrals.
4. There is one very important method. According to this method the function is brought under differential. It is especially good to them to use in cases if before introduction under differential, from function we take a derivative. Then it is put instead of dx. In such a way df(x) turns out. This way it is easily possible to achieve that even function under differential can use as a usual variable.
5. One more basic formula without which it is very often simple not to do is a formula of integration in parts: Integral(udv)=uv-Integral(vdu). This formula is effective in case it is required to find integral from performing two elementary functions in a task. Of course it is possible to use usual transformations, but it is difficult and takes a lot of time. Therefore it is much simpler to take integral by means of this formula.