Integrated notation - a basis of the mathematical analysis, one of the most difficult disciplines of a course of the higher school. It is required to solve examples with integrals both in the most mathematical analysis, and in a number of technical disciplines. All difficulty is that there is no uniform algorithm of the solution of integrals.
Instruction
1. Integration - operation, the return to differentiation. Therefore in order that it is good to integrate, it is necessary to be able to take derivatives of any functions. It is simple to learn it: there is a table of derivatives, knowing which it will be quite simple to integrate simple functions.
2. Integration of the sum of some functions can always be presented as the sum of integrals. It is especially convenient to use to these rules when functions simple, and them it is possible to calculate according to the table of the main uncertain integrals given below.
3. Very important reception - integration by a method of introduction of function under differential. It is especially convenient to it to use when introduction under differential - we take derivative of function and we put it instead of dx (that is, we have df(x)'), we try to obtain that we use function under differential as a variable.
4. One more basic formula: Integral(udv)=uv-Integral(vdu) will help us when we face integral from performing two elementary functions. It is much simpler to take integral with its help, than using transformations.