The power rule is used to find the integral of a function raised to a power. To use this rule, simply add 1 to the exponent and divide the coefficient by the new exponent.
Substitution is a method for solving integrals that involves replacing a variable in the integrand with a new variable. This new variable should be chosen so that when it is substituted into the integral, it simplifies the expression and makes it easier to integrate.
Yes, there are specific techniques for integrating trigonometric functions, such as using trigonometric identities, substitution, and integration by parts. It is important to have a good understanding of trigonometric functions and their derivatives to effectively integrate them.
Improper integrals are integrals with infinite limits of integration or integrands that are undefined at certain points. To solve these integrals, we must take the limit as the boundaries approach the undefined point or infinity. We may also need to use techniques such as partial fractions or trigonometric substitutions.
Integration by parts is a method for solving integrals that involves breaking the integrand into two parts and integrating one part while differentiating the other. This method is useful for integrating products of functions and can be applied multiple times if necessary.