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

Problem

(∫_^)(1/(2*x)*d(x))

Solution

1. Identify the constant factor in the integrand. The expression 1/(2*x) can be rewritten as 1/2⋅1/x

2. Apply the constant multiple rule for integration, which allows the constant 1/2 to be moved outside the integral sign.

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

3. Integrate the remaining function using the standard power rule for x(−1) which results in the natural logarithm of the absolute value of x

1/2*(∫_^)(1/x*d(x))=1/2*ln(x)+C

Final Answer

(∫_^)(1/(2*x)*d(x))=1/2*ln(x)+C

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