An example of how double-angle formulae can be used to help with integrating sin^2 x and cos^2 x

Demonstrates an example of integrating a function that is a product of even powers of sinx and cos x, with assistance from double-angle formulae

A more difficult example of integrating a function that is a product of even powers of sin x or cos x

A more difficult example of integrating a function that is a product of odd powers of sin x or cos x

An example of integrating a function that is a product of odd powers of sinh x or cosh x

The scheme already discussed for writing down the reults from integration by parts is applied to cyclic integration by parts where the integrand contains a product of an exponential and a sin or cosine.

We use the integration by parts scheme to address integrals with powers of x multiplied by ln(x)

An example of integrating a function that is a product of odd powers of sin x and cos x

For a quadratic equation of the form ax^2+bx+c=0, the discriminant function b^2-4ac is introduced, as a way of determining how many roots this equation has. This is then applied to problems of determining how many points of intersection the curves representing quadratic functions have.

Introduces how to use implicit differentiation to find dy/dx for an example where the chain rule is also required