Find the Antiderivative 3/x

Problem

(∫_^)(3/x*d(x))

Solution

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

(∫_^)(3/x*d(x))=3*(∫_^)(1/x*d(x))

2. Apply the power rule for the specific case of the reciprocal function, where the integral of 1/x is the natural logarithm of the absolute value of x

(∫_^)(1/x*d(x))=ln(x)+C

3. Multiply the result by the constant factor and include the constant of integration.

3*ln(x)+C

Final Answer

(∫_^)(3/x*d(x))=3*ln(x)+C

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