Integration by substitution is a technique used in calculus to simplify the integration of complex functions. It involves substituting a variable in the integrand with a new variable that makes the integration easier.
You should use integration by substitution when the integrand involves a function within a function, such as in the case of composite functions or nested functions. It is also useful when the integrand contains a function and its derivative.
The general process for integration by substitution involves three steps: identifying the substitution variable, finding the derivative of the substitution variable, and substituting the original variable and its derivative in the integrand to simplify the integration.
Some common substitution variables used in integration include u, x, t, and θ. The choice of substitution variable depends on the form of the integrand and the complexity of the function being integrated.
Yes, there are a few special cases in integration by substitution. These include using trigonometric identities to simplify the integrand, using the inverse trigonometric functions as substitution variables, and using logarithmic or exponential functions as substitution variables.
