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.

The result of some integrals will be inverse hyperbolic functions.

Hyperbolic functions are denoted by the extra h that's added onto the regular trigonometric function. Integrating these functions is similar to integrating regular trigonometric 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.

Oftentimes, evaluating the integral of a trigonometric function will be more about using another method for solving integrals, like substitution, integration by parts, or partial fractions, than it is about the trigonometric function itself.

Oftentimes, evaluating the integral of a trigonometric function will be more about using another method for solving integrals, like substitution, integration by parts, or partial fractions, than it is about the trigonometric function itself.

This example shows how to do a partial fraction decomposition with a combination of distinct linear and repeated quadratic factors.

This example shows how to do a partial fraction decomposition with a combination of distinct linear and repeated quadratic factors.

This example shows how to do a partial fractions decomposition with repeated linear factors.

This is an example of how to do a partial fractions decomposition when you're dealing with distinct quadratic factors.