# How do you find the indefinite integral of int (3/x)dx?

Nov 11, 2016

$\int \left(\frac{3}{x}\right) \mathrm{dx} = 3 \ln x + C = \ln \left(A {x}^{3}\right)$

#### Explanation:

You should remember a standard special case:

$\frac{d}{\mathrm{dx}} \ln x = \frac{1}{x} \iff \int \frac{1}{x} \mathrm{dx} = \ln x + C$

Hence, $\int \left(\frac{3}{x}\right) \mathrm{dx} = 3 \ln x + C$

NB If we write $C = \ln A$ we can also write the solution as

$\int \left(\frac{3}{x}\right) \mathrm{dx} = 3 \ln x + \ln A$
$\therefore \int \left(\frac{3}{x}\right) \mathrm{dx} = \ln {x}^{3} + \ln A$
$\therefore \int \left(\frac{3}{x}\right) \mathrm{dx} = \ln \left(A {x}^{3}\right)$