San Antonio College Library

The result of some integrals will be inverse hyperbolic functions.

There's a trick to integrating the product of a higher-degree tangent function and a higher-degree secant function. This is an example in which the power of the secant function is even. To use this method, the power of the tangent function can be even or odd.

We'll use a tangent substitution in this example to simplify the integral.

When you have to find the limit of trigonometric functions, there are special trig limit formulas you'll want to use in order to simplify your function to a point where you can evaluate its limit.

Trigonometric substitution problems are often long and tedious, with lots of important details that you have to pay attention to. It's easier to work through trig sub problems if you have everything you're going to need ahead of time, which is why I like to go through this setup process before I start the main part of the problem.

We'll talk about the derivatives of each of the six trigonometric functions, how to apply chain rule when finding the derivatives of trig functions, and how to find the derivatives of higher-order trigonometric functions using power rule and chain rule.