 Type 5.Other rational expressions with the irrational function
1. If , we can use .
2. If , we can use .
3. If can be factored as , we can use .
4. If and can be factored as , we can use
Frequently occuring integrals of irrational functions are: , where and is possitive on an interval. We can exclude the case, that the polynomial has a double root.
Taking the factor (if ) or (if ) we reduce the integral to the form or , leading (by means of substitution) to the integrals:
or , respectively.
3. Integration of TRIGONOMETRIC functions
1. Given an integral , i.e. the integrand is a rational function in terms of and . By the substitution the integral is reduced to an integral of a rational function. If , then , , and .
2. If = , then .
3. If =  , then .
If = , then .
4. , ò and ï – even nonnegative integers, then , .
5. For integrals we use following formulas:
6. , then and .
Date: 20150102; view: 1227
