How to Integrate Using Trig Substitutions

Hi, my name is Stefan. Today, I'm going to be speaking on how to integrate using trig substitutions. Let's say for example we have the integral of X cubed/ the square root of 16 - X squared. There's a trig substitution that says if you have the square root of A squared - X squared that you let X = A sine theta. Now in substituting this in we get the integral of 4 sine theta cubed/the square root of 16 which is 4 squared - 4 sine theta quantity squared and our DX is 4 cosine theta, D theta. Now, this is good because if you look at our denominator you see a 1 - sine squared which of course = cosine squared and this allows us to simplify and then in our answer we get 4 squared times 16 - X squared + 16 - X squared quantity cubed + C/3. And that's how you integrate using trig substitutions.