# Find: {eq}\displaystyle \int \dfrac 2 x\ dx {/eq}.

## Question:

Find: {eq}\displaystyle \int \dfrac 2 x\ dx {/eq}.

## Integrals

Integration is also known as anti-differentiation, and as the name implies, it is the reverse operation of differentiation or derivatives. It can either be definite or indefinite, the difference of which the former has boundaries for integration while the latter uses an arbitrary constant in the result.

We are given the integral {eq}\displaystyle \int \frac{2}{x}dx {/eq} and we are asked to solve this integral.

\begin{align*} \int \frac{2}{x}dx &= 2\int \frac{dx}{x}\\ &= 2\ln(x) + c \end{align*}

Therefore, the integral is equivalent to {eq}2\ln(x) + c {/eq} where {eq}c {/eq} is an arbitrary constant.