What is chain rule integration?

The term chain rule integration refers to the integration technique that reverses the process of differentiating using the chain rule. Chain rule integration is more commonly known as the substitution or change in variable techniques of integration.

The basic idea of using the chain rule in differentiation is du = u'(t) dt. For example, in the equation for the integral of cos(3t^2) * 6t dt, the variable u is used to describe 3t^2, and u' is equal to 6t. Therefore, du = 6t dt. Since the cos(u) du is equal to sin(u) + c, the resulting formula substitutes 3t^2 for u. The final equation is sin(3t^2) + c.