Integration is one of the basic operations of calculus. However, its results are not always straightforward; there are some integrals whose solution is not apparent by inspection. Because this is the case, and because closed form and numerical solutions are valuable in many cases, mathematicians have developed several different methods of integration.

In many cases, the integral may be evaluated at all points by direct anti-differentiation. The rules of differentiation are then followed backwards to find a closed form solution of the integral in question. When a definite integral is desired in this case, the anti-differentiated form is simply evaluated at the limits.

In some cases, an apparently difficult integral can be vastly simplified by "u-substitution." In u-substitution, the integral is shifted from the original x variable to a new variable, u, with the limits (if any) changed appropriately and appropriate attention given to...