Find the Antiderivative 2/x

Problem

(∫_^)(2/x*d(x))

Solution

1. Identify the integral form by moving the constant coefficient outside the integral.

(∫_^)(2/x*d(x))=2*(∫_^)(1/x*d(x))

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

2*(∫_^)(1/x*d(x))=2*ln(x)+C

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

2*ln(x)+C

Final Answer

(∫_^)(2/x*d(x))=2*ln(x)+C

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