Integration using Computer Algebra Systems (CAS): Example 1

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In this video I go over an example on using computer algebra systems (CAS) and use an online CAS to solve the integral of the function x(x^2+2x+4)^(1/2). This was the same example I had solved earlier using tables of integrals and that video can be seen in the video links below. The resulting answer from both the tables of integrals and the online CAS appear different at first but I show that this is common and both can be rewritten so that the answers are identical in form. Also in this example I show that sometimes when rewriting the answer to another, there may be an additional constant appearing in the answer but since it is just a constant it can be absorbed into the all-encompassing constant of integration. This is a very important video to watch for those that may have questions about why a computer produces different answers than if they were to integrate by hand!


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Integration using Computer Algebra Systems (CAS): Example 1

Integration using CAS Example 1.jpeg

Use a computer algebra system to find:

Solution:

In my earlier video on solving integrals using Tables of Integrals, I had solved this integral already and the answer was:

If we use an online CAS we get the following:

Although this answer looks different than the one we solved earlier, they are equivalent after rewriting the answer and using the following hyperbolic trigonometric identity (see my earlier video for the proof; link in this video description):

Important Notes:

  • As can be seen from this example the way a computer solves an integral can differ from solving by hand as well as from different CAS programs and thus the final answers although appear different are still the same and can be rewritten both ways.

  • Also the constant of integration includes all constants so any leftover constants when rewriting the resulting answer can be simply be absorbed into the constant of integration and thus the answer is still the same.



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