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);
To evaluate the integral use the command value.
Symbolic Differentiation with Maple
The inert differentiation operator is Diff:
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);
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);