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