Integration by substitution, also known as u-substitution, is a method used to evaluate integrals that involve a composite function. It involves substituting a variable u for part of the function and then using the chain rule to simplify the integral.
Integration by substitution is useful when the integrand (the expression being integrated) is a composite function, meaning it can be broken down into two or more simpler functions. It is also helpful when the integrand contains a function and its derivative, or when the integrand contains a function raised to a power.
To perform integration by substitution, follow these steps:
Integration by substitution allows us to evaluate integrals that would otherwise be difficult or impossible to solve. It simplifies the integrand and makes the integration process more manageable. It is also a useful tool for solving a wide range of problems in calculus and physics.
Integration by substitution may not always work for every integral. Some integrals may require more advanced techniques, such as integration by parts or partial fractions. Additionally, substitution can only be used for integrals with a composite function, so it may not be applicable in all cases.