Integral of 1/x

Q: What is the integral of 1/x?

\int \frac{1}{x}\,dx = \ln\left(\left|x\right|\right) + C.

Q: How can I check the answer?

Differentiate it: the derivative of \ln\left(\left|x\right|\right) is \frac{1}{x}. CalcViz checks every antiderivative this way before showing it.

\int \frac{1}{x}\,dx = \ln\left(\left|x\right|\right) + C

The one power the power rule cannot handle (it would divide by zero). The antiderivative is ln|x|, and the absolute value makes it valid for negative x too.

Step by step

Reciprocal rule
∫1/u du = ln|u|.
$\int \frac{1}{x}\,dx = \ln\left(\left|x\right|\right)$

f(x) = 1/x
F(x) + C

Constant C = 0.0

Every choice of C gives a valid antiderivative, since shifting up or down doesn’t change the slope.

Open in the integral calculator

Questions students ask

What is the integral of 1/x?

$\int \frac{1}{x}\,dx = \ln\left(\left|x\right|\right) + C$ .

How do you integrate 1/x?

The one power the power rule cannot handle (it would divide by zero). The antiderivative is ln|x|, and the absolute value makes it valid for negative x too.

How can I check the answer?

Differentiate it: the derivative of $\ln\left(\left|x\right|\right)$ is $\frac{1}{x}$ . CalcViz checks every antiderivative this way before showing it.