# What is the integral of ln(7x)?

Dec 9, 2014

Integration by Parts

$\int u \mathrm{dv} = u v - \int v \mathrm{du}$

Let $u = \ln \left(7 x\right) \text{ }$ $\text{ } \mathrm{dv} = \mathrm{dx}$
$\implies \mathrm{du} = \frac{\mathrm{dx}}{x} \text{ }$ $\text{ } \implies v = x$

By Integration by Parts,

$\int \ln \left(7 x\right) \mathrm{dx} = \ln \left(7 x\right) \cdot x - \int x \cdot \frac{\mathrm{dx}}{x}$

$= x \ln \left(7 x\right) - \int \mathrm{dx} + C$

$= x \ln \left(7 x\right) - x + C$

I hope that this was helpful.