Using trig substitution or partial fractions?

[JessicaJ283782]

When would you use trig substitution vs. partial fractions? I know partial fractions is when you have a polynomial over a polynomial, but some of the problems in the trig substitution section in my book had polynomial over polynomial and used trig substitution?

 

[alan2]

A good general rule is that any time you see the sum or difference of 2 squares you should think trig substitution. The sum or difference of 2 squares looks like the Pythagorean theorem so you have a right triangle. Label an angle and express all terms as trigonometric functions of that angle. There certainly are multiple methods for many integrations.