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

Problem

(∫_^)(2/(x−2)*d(x))

Solution

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

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

2. Identify the form of the integral, which matches the rule (∫_^)(1/u*d(u))=ln(u)+C

(∫_^)(1/(x−2)*d(x))=ln(x−2)+C

3. Multiply the result by the constant factor of 2 that was moved outside the integral.

2*ln(x−2)+C

Final Answer

(∫_^)(2/(x−2)*d(x))=2*ln(x−2)+C

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