This part of the site is useful for the next page : the integrals. |

In general :

If u is a function, an antiderivative of is , and an antiderivative of is . For the calculation, you also have to know that the antiderivative of a sum of functions is equal to the sum of the antiderivatives of the functions, and that if alpha is a real number, an antiderivative of is .

In the examples above, you simply apply the general formula of a antiderivative of a power of x. Below we are going to use the formulas of the exponential and logarithm functions, and to do this we 'll have to modify f. Suppose , then we have . Above we managed to express f functions of u and its derivative. Thus finally :

Last example,

Suppose , then and hence : .