Evaluate the Integral integral of (cos(x))/x with respect to x

Problem

(∫_^)(cos(x)/x*d(x))

Solution

1. Identify the integral as a non-elementary integral. The function cos(x)/x does not have an antiderivative that can be expressed in terms of basic algebraic, trigonometric, or exponential functions.

2. Define the special function used to represent this specific integral, which is known as the Cosine Integral, denoted as Ci(x)

3. Apply the definition of the Cosine Integral to express the result.

Final Answer

(∫_^)(cos(x)/x*d(x))=Ci(x)+C

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