In this video I go over an example on trig substitution for integrals and solve for the integral of the function sqrt(9-x²)/x². In this example I write the variable x in terms of a sine function to simplify the integral by removing the square root.

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Trigonometric Substitution for Integrals: Example 1

Example:

Solution:

Since this is an indefinite integral, we must return to the original variable x. This can be done by using trigonometric identities to express cotѲ in terms of sinѲ = x/3 or by drawing a diagram where Ѳ is considered as the angle of a right triangle. The latter is usually easier and we will try that:

Note: Although Ѳ > 0 in the diagram, this expression for cotѲ is valid even when Ѳ < 0.