Question

How do you find the antiderivative of `f(x)=x^5`?

Answer 1

Have a look:

Explanation:

You are looking for a function that once derived will give you `x^5`;
a good candidate would be `x^6` in fact if you derive it you get: `6x^5`.
it is not really equal but we can use a little trick and say (to get rid of the `6`) that our antiderivative will be:
`F(x)=1/6x^6+c`
the `c` is a constant that we add to be sure to cover all the possibilities and anyway, during the derivation, it will desappear (our antiderivative could be, for example, `F(x)=1/6x^6+7` or `F(x)=1/6x^6+345` or other number so that when you derive it you will still get `x^5`!!!).

As a general rule the antiderivative of `x^n` can be found as:

`x^(n+1)/(n+1)+c`