 So, let's take a look at the integration of other trigonometric functions. Some of these are based on other trigonometric identities. One of the important are the angle addition identities. Sine of x plus or minus y is sine x cosine y plus or minus cosine x sine y, and cosine of x plus or minus y is cosine x cosine y minus or plus sine x sine y. And this gives us some useful identities. For example, what is sine of x plus y plus sine of x minus y? Well first, sine of x plus y is sine x cosine y plus cosine x sine y, and sine of x minus y is sine x cosine y minus cosine x sine y. But this simplifies, and that tells me this product sine x cosine y can be expressed as a sum of two sine functions. And if we do this for the other compositions, we find the following identities that allow us to transform a product of sines and cosines into a sum of sines and cosines. And as our good friend Leonard Euler points out, these should actually be proven. And we'll leave those as exercises. With these identities, we can evaluate the integrals of products of sines and cosines. For example, the integral of sine three x cosine two x, well we know that sine x cosine y can be expressed as a sum of sines, so let's go ahead and rewrite that. And I can simplify this. And because this is a definite integral of sines, I can evaluate those directly. And don't forget the constant of integration. How about sine squared of x? Sine squared of x is sine of x times sine of x. And so we can use the product of sines, which is going to correspond to a difference of cosines, which we can simplify, integrate, and add our constant of integration.