# Maple/Using Maple in Calculus, PDEs, and ODEs

## Symbolic Integration with Maple

Tired of looking up tables of integrals? In case you don't have access to Maple, here's a cheatsheet that is extremely useful for your reference: Tables of Integrals, Trig Identities, Advanced Mathematics, and much more

Want to check the correctness of your hand-worked solution? Want an easy way to generate/learn mathematical LaTeX?

To make sure that the typed integral is right, before asking Maple to actually evaluate it, use the inert command Int:

>Int((cos(omega*t + phi))^2,t=0..2*Pi/omega);

$\int _{0}^{2\pi /\omega }{\cos(\omega t+\phi )}^{2}dt$

To evaluate the integral use the command value.

>value(%);

${\frac {\pi }{\omega }}$

## Symbolic Differentiation with Maple

The inert differentiation operator is Diff:

>Diff(ln(x),x);

${\frac {d}{dx}}\ln(x)$
>value(%);

${\frac {1}{x}}$

## Solving partial fraction decompositions with Maple

A borrowed trick from Matlab (using the fundamental theorem of calculus):

To integrate it, it will probably have to do a partial fraction expansion, so we let it do the expansion when it integrates, then differentiate to get our rational expression converted/decomposed into partial fractions:

>diff(int((5*x+1) / (x^2-1),x),x);

${\frac {3}{x-1}}+{\frac {2}{1+x}}$

Maple has partial fraction expansion built in, though, if you want to do it directly. The command is

>convert( (5*x+1) / (x^2-1), parfrac, x);

${\frac {3}{x-1}}+{\frac {2}{1+x}}$