How can you find the integral of x^-1

The traditional rule for integration of a variable raised to a power is to raise the power by 1 and divide the answer by that new exponent. However, this rule leads to an answer of x^0 = 1, which can't be right. It's not. The integral of x^-1 = 1/x is the natural logarithm of x, or lnx. Likewise, the derivative of lnx is x^-1, and this is an especially important rule to remember for things like differential equations in the future.