The most frequently asked question about integration is how to determine which technique to use for a given problem. There is no one-size-fits-all approach, and the choice of technique will depend on the form of the function being integrated.
Indefinite integration is the process of finding a general solution to an integral, while definite integration is finding a specific value for an integral over a given interval. In other words, indefinite integration results in a function, while definite integration results in a numerical value.
Substitution is a commonly used technique in integration, particularly for functions that contain nested functions or variables raised to a power. It involves replacing a variable with a new expression in order to simplify the integral. Substitution is often a good choice when the integral contains a function and its derivative.
Integration by parts is another commonly used technique that allows you to integrate the product of two functions. It involves using the product rule in reverse, and can be useful for integrating functions that contain a product of functions that do not have an obvious antiderivative.
The best way to improve your integration skills is through practice. Start with simpler integrals and work your way up to more complex ones. You can also try using online resources and textbooks to find a variety of practice problems and solutions. Remember to also review the different techniques and when they are most appropriate to use.