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

##### 1 Answer

Nov 5, 2016

Rewrite as

#### Explanation:

We first need to recognize that

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:

This is equivalent to

As usual, you can check this answer by taking the derivative, which gives you