Evaluate the Integral integral of 1/(2x) with respect to x

Problem

(∫_^)(1/(2*x)*d(x))

Solution

1. Factor out the constant coefficient from the integrand to simplify the expression.

(∫_^)(1/(2*x)*d(x))=1/2*(∫_^)(1/x*d(x))

2. Apply the integration rule for the reciprocal function, which states that the integral of 1/x is ln(x)

1/2*(∫_^)(1/x*d(x))=1/2*ln(x)+C

3. Include the constant of integration C to represent the family of all possible antiderivatives.

1/2*ln(x)+C

Final Answer

(∫_^)(1/(2*x)*d(x))=1/2*ln(x)+C

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