Write the mathematical expression that represents the integration process. Use the symbol of an elongated S to represent the process of integration. Write the term YdX to the right of the elongated S so the expression appears as SYdX. A mathematical expression in this form is read as the integral of Y with respect to X.
Move Y to the left of the elongated S. Y is always treated as a constant if it is not given as a function of the variable X. By moving Y to the left of the integral sign, you are indicating that Y is not dependent on X and will therefore not be included in the integration process. Rather, Y will be multiplied by the result of the integration process. The mathematical expression becomes Y x (SdX). The expression is read as Y multiplied by the integral of dX.
Integrate dX. The result of integrating dX is X. Replace SdX with X.
Multiply X by the constant Y. The mathematical expression becomes Y x (X).
Add the integration constant C to the expression. The constant C represents an arbitrary constant value associated with an indefinite integral. The symbol C must be included for mathematical correctness. The result of integrating Y with respect to X is YX + C.