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
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: