# How do you find the antiderivative of f(x)=x^4-5x^3+2x-6?

Nov 20, 2016

$= {x}^{5} / 5 - \frac{5}{4} {x}^{4} + {x}^{2} - 6 x + C$

#### Explanation:

The antiderivative of $f \left(x\right)$ is determined by applying
$\text{ }$
the antiderivate of polynomial rule.
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The antiderivative of a polynomial ${x}^{n}$ where $n$ is an integer is:
$\int {x}^{n} \mathrm{dx} = {x}^{n + 1} / \left(n + 1\right) + C$
$\text{ }$
$\int {x}^{4} - 5 {x}^{3} + 2 x - 6$
$\text{ }$
$= {x}^{5} / 5 - \frac{5}{4} {x}^{4} + {x}^{2} - 6 x + C$

Nov 20, 2016

$f \left(x\right) = {x}^{4} - 5 {x}^{3} + 2 x - 6$

Let $F \left(x\right)$ be the antiderivative of $f \left(x\right)$, and $C$ is a constant.
$F \left(x\right) = \frac{1}{5} {x}^{5} - \frac{5}{4} {x}^{4} + {x}^{2} - 6 x + C$