Integral of $$$\frac{1}{v}$$$

The calculator will find the integral/antiderivative of $$$\frac{1}{v}$$$, with steps shown.

Find $$$\int \frac{1}{v}\, dv$$$.

The integral of $$$\frac{1}{v}$$$ is $$$\int{\frac{1}{v} d v} = \ln{\left(\left|{v}\right| \right)}$$$:

$${\color{red}{\int{\frac{1}{v} d v}}} = {\color{red}{\ln{\left(\left|{v}\right| \right)}}}$$

Therefore,

$$\int{\frac{1}{v} d v} = \ln{\left(\left|{v}\right| \right)}$$

Add the constant of integration:

$$\int{\frac{1}{v} d v} = \ln{\left(\left|{v}\right| \right)}+C$$

$$$\int \frac{1}{v}\, dv = \ln\left(\left|{v}\right|\right) + C$$$A

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