Evaluate the Integral integral of 2/x with respect to x

Problem

(∫_^)(2/x*d(x))

Solution

1. Identify the constant in the integrand and move it outside the integral.

(∫_^)(2/x*d(x))=2*(∫_^)(1/x*d(x))

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

(∫_^)(1/x*d(x))=ln(x)+C

3. Combine the constant multiplier with the result of the integration.

2*ln(x)+C

Final Answer

(∫_^)(2/x*d(x))=2*ln(x)+C

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