In this video I go over another example on integration of rational functions by partial fractions and this time integrate a function that has a non-reducible non-linear factor in the denominator. This requires applying the method of partial fraction decomposition but for non-linear factors as I have shown in my earlier videos. The example I go over is the integral of (2x² - x + 4)/(x³ + 4x). In the example I derive the integral of 1/(x² + a²) = 1/a * inverse tan (x/a) which was required in solving the overall integral.

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Integration of Rational Functions by Partial Fractions: Example 5

Example:

Solution: