In this video I go over the use of computer algebra systems (CAS) and how they are used to calculate integrals very quickly. From my earlier videos on using Tables of Integrals I showed that integration can be seen as simply mixing and matching the integrand to match the form given in the Tables of Integrals. Computers are very good at matching patterns so it is not surprising that CAS can be used to quickly solve many integrals. In this video I introduce this topic but show that although CAS are very useful, integrating by hand is still important and comes in handy for some integrals as will be shown in later example videos. Also it is important to note that some CAS omit the integration constant as well as the absolute value signs in integrals involving logarithms so it is always important to understand the answer that a CAS outputs.

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Integration using Computer Algebra Systems (CAS)

In my earlier videos on integration using tables of integrals, I showed we can us solve the integral by simply matching the form of the integral with the forms in the tables.

• Sometimes we need to use substitutions to transform the form of the integral to match the form in the table

Computers are very good at matching patterns and can be programmed to use substitutions to match the integrals to those stored in the computer program.

• This type of computing program is called a Computer Algebra System (CAS)
• There are many free online CAS websites

Although CAS are very good at integration this doesn't mean that integration by hand is an obsolete skill.

• In my later videos I will go over some examples that show integration by hand produce a much more convenient answer than that of CAS

To get an idea of how a computer integrates functions, let's consider the following integral:

No let's see what happens if I integrate by using a CAS:

Important Notes:

• Some CAS omit the constant C so you may need to add the constant.
• In our integral, the CAS left out the absolute value signs for the natural log.
  • This is fine if we are only considered with the values: x > 2/3
  • But if we are interested in all values of x then we need to add the absolute value signs.

I will go over some more examples in my later videos, so stay tuned!