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 x³/(4x²+9)^3/2 and first complete the square inside the denominator before using trig substitution to solve the integral.

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Trigonometric Substitution for Integrals: Example 6

Example:

Now this is still not in the form that we know from our trig substitution tables. But we can rewrite it further: