Integration by Partial Fractions: Example 6

in mathematics •  2 months ago  (edited)

In this video I go over another example on integration of rational functions by partial fractions and this time go over an example that involves a non-linear function in the denominator that can't be factored any further. The example is on solving the integral of (4x2-3x+2)/(4x2-4x+3) and from this example we are able to obtain a general procedure for these types of integrals which end up being in the form of natural logs and inverse tangent functions.

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Integration of Rational Functions by Partial Fractions: Example 6

Integration by Partial Fractions Example 6.jpeg



Thus we can't reduce further.

We also can't use partial fraction decomposition because we will get back to the same place we started, for example:

We can try completing the square instead:

Note: This example illustrates the general procedure for integrating a partial fraction of the form:

We complete the square in the denominator and then make a substitution that brings the integral into the form:

Then the first integral is a logarithm and the second is expressed in terms of tan-1.

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