Let us recall the derivatives of elementary functions. For instance, the power rule states that

.

This formula can be transformed as follows.

First, substitute  (n + 1)  for  k :

.

Then divide both sides of the equality by  (n + 1)  (provided that n ≠ –1) and read the formula from right to left:

.

Therefore, the function    is a primitive of  xn , so the power rule for integration has the following form:

,   .

The derivatives of all elementary functions can be treated similarly to transform the table of derivatives to the table of integrals.

Indefinite Integrals Definite Integrals Differential Equations