Evaluating integrals is much more difficult than evaluating derivatives. For derivatives, there is a systematic procedure based on the chain rule that effectively allows any ...

This does an integral over the interior of the unit circle. Here is an equivalent form. Even though an integral may be straightforward over a simple rectangular region, it ...

In calculus even more than other areas, Mathematica packs centuries of mathematical development into a small number of exceptionally powerful functions. Continually enhanced ...

Even more so than for other special functions, you need to be very careful about the arguments you give to elliptic integrals and elliptic functions. There are several ...

Now that we have introduced the basic features of patterns in Mathematica, we can use them to give a more or less complete example. We will show how you could define your own ...

Numerical sums, products and integrals. Here is a numerical approximation to ∑_(i=1)^∞((1)/(i^3)). NIntegrate can handle singularities in the integration region.

CosIntegral[z] gives the cosine integral function Ci(z).

CoshIntegral[z] gives the hyperbolic cosine integral Chi(z).

LogIntegral[z] is the logarithmic integral function li(z).

Numerical integration functions. This finds a numerical approximation to the integral ∫_(0)^∞ e^-x^3 x. Here is the numerical value of the double integral ∫_(-1)^1 dx ...