In this video I go over another example on using CAS to solve integrals and this time solve the integral of the function x+60sin⁴(x)cos⁵(x). In this example I also show how CAS can be used to graph functions and their integrals and even derivatives. From the graphs I show how to find the extreme points in terms of local minimum and maximum as well as find the inflection points. This is an important video to watch because it shows how powerful computers can be for solving and graphing very complex integrals.

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Integration using Computer Algebra Systems (CAS): Example 4

If f(x) = x + 60sin⁴(x)cos⁵ (x), find the antiderivative F of f such that F(0) = 0.

Graph F for 0 ≤ x ≤ 5. Where does F have extreme values and inflection points?

Solution:

To obtain the extreme points, we need to graph its derivative and find when it is equal to 0:

To find the inflection points we need to graph the second derivative of F, and we can look for a CAS that solves derivatives online for that: