What is the integral of \frac{\sin(x)}{x}?


What is the integral of {eq}\frac{\sin(x)}{x}? {/eq}

Indefinite Integral:

Indefinite integration is the reverse process of differentiation. It is therefore sometimes referred as anti differentiation. There are various integration rules, such as the difference rule, sum rule, power rule, constant rule, trigonometric rules etc., that can be applied while figuring an indefinite integral in addition to the rule of anti derivatives differing by constant. To solve the given problem, we have used one of the rules mentioned above.

Answer and Explanation:

Given: $$\displaystyle \int \frac{\sin(x)}{x} $$

Let's use the non-elementary integral:

{eq}\displaystyle \int \frac{\sin(x)}{x}dx =Si(x) {/eq}

$$\displaystyle =Si(x) $$

Add a constant to the solution, and we'll have the final outcome:

$$= \boxed{Si(x) + C} $$

Learn more about this topic:

Indefinite Integrals as Anti Derivatives

from Math 104: Calculus

Chapter 12 / Lesson 11

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