Question

What is the antiderivative of `1/x^4`?

Answer 1

`-1/3x^-3+C`

Explanation:

I would begin by rewriting the expression as `x^-4`.

We then have:

`intx^-4dx`.

To integrate or take the anti-derivative, we do the opposite of what we would do if we were taking the derivative; instead of bringing down the power and reducing it by `1`, we will add one to the power and multiply what is now the integrand by the reciprocal of the power.

`=>-1/3x^-3`

To account for any constants we might have lost when the derivative was taken (the derivative of a constant is zero), we add a general constant, `C`.

`=>-1/3x^-3+C`

This is equivalent to

`-1/(3x^3)+C`