Advanced Integration

In addition to basic integration techniques, advanced integration techniques are often necessary and/or more efficient in reaching the desired solution. One technique is integration by parts, a process that finds the integral of a product of functions in terms of the integral of the product of their derivative and antiderivative. Another example is integration by substitution, also known as u-substitution, the reverse chain rule, or change of variables. This is the counterpart to the chain rule for differentiation, which can loosely be thought of as using the chain rule “backward.”