Evaluate the Integral

Problem

(∫_1^3)(2/x*d(x))

Solution

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

(∫_1^3)(2/x*d(x))=2*(∫_1^3)(1/x*d(x))

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

2*(∫_1^3)(1/x*d(x))=2*[ln(x)]31

3. Evaluate the definite integral by substituting the upper limit and subtracting the value at the lower limit.

2*[ln(x)]31=2*(ln(3)−ln(1))

4. Simplify the expression using the property that ln(1)=0

2*(ln(3)−0)=2*ln(3)

Final Answer

(∫_1^3)(2/x*d(x))=2*ln(3)

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