Question

How do you integrate `int 1/x^3dx`?

Answer 1

Rewrite as `intx^-3dx` and take the anti-derivative.

Explanation:

We first need to recognize that `1/x^3` is equivalent to `x^-3`.

Once we get that far, the problem becomes quite simple to solve.

Do be careful, however, as we are dealing with a negative exponent, so when we add one to the power as we take the anti-derivative, the magnitude of the power will decrease. This also means that our constant will have to be negative as well, since the x term in the integral is positive. Taking the anti-derivative, we get:

`-1/2*x^-2 +C`

This is equivalent to `-1/(2x^2) +C`

As usual, you can check this answer by taking the derivative, which gives you `x^-3`.