Integration by Partial Fractions: Example 9: Rationalizing Substitutions

in mathematics •  2 months ago  (edited)

In this video I go over another example on integrating rational functions using partial fractions and this time show how sometimes even if the function we are integrating is a non-rational function we may be able to rationalize it or make it into a rational function using an appropriate substitution and thus be able to use partial fractions. The example I cover in this video is the integral of the function sqrt(x+4)/x and show how we can use the substitution u = sqrt(x+4) to transform the non-rational function into a rational function. This is a very useful technique to have when integrating non-rational functions so make sure to watch this video!

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Integration of Rational Functions by Partial Fractions: Example 9: Rationalizing Substitutions

Integration by Partial Fractions Example 9.jpeg

Some nonrational functions can be changed into rational functions by appropriate substitutions.

In particular, when the integrand contains an expression of the form:

Then the following substitution may be effective:



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