Definite integration with additional complexities

Definite integration is more difficult to use in Maple than is indefinite integration. Indefinite integration is simply antidifferentiation and transforms one function, the integrand, into another function, the indefinite integral. In the case of definite integration, the area under the function must be somehow computed and the value of this area will depend upon the properties of the parameters in the integrand. Because Maple assumes nothing about parameters that are used in expressions, you have to tell Maple what are the special properties of these parameters so that Maple can better interpret your commands and give you the answers that you are looking for.

The properties of parameters in Maple expressions and equations can be specified using the assume command.

assume(n, integer)
assume(m >= -1)

Use the ?assume command to learn more about this powerful command.

Very often when doing indefinite integrals you will need to tell Maple as much as you can about the parameters so that Maple can give you the best result.

Maple is also able to do definite integrals between arbitrary symbolic limits, as in

int(integrand, x=a..b)

and Maple can do integrals over infinite limits

int(integrand, x=0..infinity)

In all of these cases of course it is necessary for the integral to be doable in symbolic form. However Maple is extremely powerful in finding the integrals of complex expressions.