Trigonometric Substitution for Integrals: Example 6

In this video I go over another example on trig substitution for integrals and this time show that sometimes we need to further simplify the integrand to enable trig substitution to be used. In this example I solve the integral of the function x^3/(4*x^2+9)^(3/2) and first complete the square inside the denominator before using trig substitution to solve the integral.

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I don't always use trig substitution for integrals but when I do I usually complete the square first ;)