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.

Answer and Explanation: 1

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.


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Indefinite Integrals as Anti Derivatives

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Chapter 12 / Lesson 11
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Indefinite integrals, an integral of the integrand which does not have upper or lower limits, can be used to identify individual points at specific times. Learn more about the fundamental theorem, use of antiderivatives, and indefinite integrals through examples in this lesson.


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