# What is int lnx^2 / lnx^3?

Nov 14, 2015

$\int \ln \frac{{x}^{2}}{\ln} \left({x}^{3}\right) \mathrm{dx} = \frac{2 x}{3} + c$

#### Explanation:

Well, when integrating you should always have $d \left[a r g\right]$, where [arg] is a variable, it's like $\int$ is "(" and that is the ")". It's more important because it tell us with which variable you want us to integrate.

In this case it's pretty clear that's $x$ but as a general rule it's important to specify.

Anyhow, using the property of logarithms we have

$\int \ln \frac{{x}^{2}}{\ln} \left({x}^{3}\right) \mathrm{dx} = \int \frac{2 \ln \left(x\right)}{3 \ln \left(x\right)} \mathrm{dx} = \int \frac{2 \mathrm{dx}}{3} = \frac{2 x}{3} + c$

Assuming $x \in \mathbb{R} , x > 0 , x \ne 1$ so as to avoid complex numbers when doing those algebrisms and/or having the function defined in the reals at those points.