Setting Up Partial Fractions When You Have Repeated Linear Factors
Substituting with Expressions of the Form f(x) Multiplied by h(g(x))
How to Integrate a Function Multiplied by a Set of Nested Functions

Knowing When to Avoid Trigonometry Substitution

It’s useful to know when you should avoid using trig substitution. With some integrals, it’s better to expand the problem into a polynomial. For example, look at the following integral:

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This may look like a good place to use trig substitution, but it’s an even better place to use a little algebra to expand the problem into a polynomial:

image1.png

Similarly, look at this integral:

image2.png

You can use trig substitution to evaluate this integral if you want to. (You can also walk to the top of the Empire State Building instead of taking the elevator if that tickles your fancy.) However, the presence of that little x in the numerator should tip you off that variable substitution will work just as well:

image3.png

Using this substitution results in the following integral:

image4.png

Done!

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Integrating Powers of Cotangents and Cosecants
Find the Integral of Nested Functions
How to Integrate Even Powers of Sines and Cosines
Setting Up Partial Fractions When You Have Distinct Linear Factors
Setting Up Partial Fractions When You Have Repeated Quadratic Factors
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