This is documentation for Mathematica 5.2, which was
based on an earlier version of the Wolfram Language.
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Integrals, Sums and Products

Mathematica has unprecedented calculus capabilities. Here are a few of the integrals, sums and products that it can do.

Indefinite Integrals

Definite Integrals

Checking Integrals

To check an indefinite integral, you can differentiate the result you get.

Here is an integral.

D differentiates the integral, and recovers the original integrand.

Here is another integral.

Differentiating the integral gives a result in a slightly different form.

Applying Simplify recovers the original integrand.

Here is a definite integral.

This finds a numerical approximation to the result.

You can use NIntegrate to do the integral numerically from the start.

Sums and Products