Integration using substitution is a technique used in calculus to find the antiderivative of a function. It involves substituting a variable or expression in the integrand with a new variable or expression to simplify the integral.
You should use substitution for integration when the integrand contains a complicated expression or function that can be simplified by substituting a variable or expression. This method is also useful when dealing with trigonometric functions or exponential functions.
The process for integration using substitution involves choosing a new variable or expression to substitute in the integrand, differentiating it to find its differential, and then replacing the original variable in the integrand with the new variable and its differential. This can help simplify the integral and make it easier to solve.
One tip for choosing the correct substitution is to look for patterns in the integrand. For example, if the integrand contains a polynomial function, it may be helpful to substitute with the highest degree term. Another tip is to try using trigonometric identities for integrals involving trig functions.
No, substitution may not work for all integrals. Some integrals may require other integration techniques such as integration by parts or partial fractions. It is important to consider all available methods and choose the most appropriate one for each integral.