Question

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

Answer 1

`=x^5/5-5/4x^4+x^2-6x+C`

Explanation:

The antiderivative of `f(x)` is determined by applying
`" "`
the antiderivate of polynomial rule.
`" "`
The antiderivative of a polynomial `x^n` where `n` is an integer is:
`int x^n dx = x^(n+1)/(n+1)+C`
`" "`
`intx^4-5x^3+2x-6`
`" "`
`=x^5/5-5/4x^4+x^2-6x+C`

Answer 2

`f(x)=x^4-5x^3+2x-6`

Let `F(x)` be the antiderivative of `f(x)`, and `C` is a constant.
`F(x)=1/5x^5-5/4x^4+x^2-6x+C`