Software for symbolic calculus?

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Its more of a reference than a question, recently i am doing too much integration within integration and derivatives within derivatives and limits of long string of functions and too much math for wolfram to handle on a laptop, so is there a better program for integration and derivatives and limits or is there something online that could handle and calculate a limit of long string of functions ?!

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Sage is a great open-source resource for doing all kinds of math. It is freely available and you can try it in your browser here. It helps if you know Python.

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If you have a look here, you will have the list of currently available computer algebra systems, their cost and type of license.

Maxima, SageMath and Mathics are, at least in my opinion, very good choices for what you seem to need (all of them are free).