**Integration of polynomial functions**

Let's start by going through different functions and looking at rules for their integration. Let's start with the integral rule of the power function:

The result is generally valid whenever the original function is defined. However, at this stage, let us consider only the situation where* r = 1,2,3,4,â€¦.* that is,* r *is a positive integer. [Check this rule yourself by deriving the expression to the right of the equation!].

If the function has no variable at all (the power of *x* is zero), a simpler memory rule can be used

Combined with the integral rule of the sum mentioned in the previous chapter, we can now calculate the integrals of polynomial functions.

**Example 1**: Integrate

The rules should be used as much as possible before integrating separate terms, often the expression to be integrated is significantly simplified and there is less to be calculated.

**Example 2**: Find the integral

In addition, it is worth noting that if there is a parentheses expression inside the integral, it must first be opened before the integral can be calculated.

**Example 3**:

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