Find the Integral 3/x

Problem

(∫_^)(3/x*d(x))

Solution

1. Identify the constant in the integrand. The expression 3/x can be rewritten as 3⋅1/x

2. Apply the constant multiple rule for integration, which allows the constant 3 to be moved outside the integral sign.

(∫_^)(3⋅1/x*d(x))=3*(∫_^)(1/x*d(x))

3. Apply the power rule for the specific case of 1/x The integral of 1/x is ln(x)

3*(∫_^)(1/x*d(x))=3*ln(x)+C

4. Add the constant of integration C to represent the family of antiderivatives.

Final Answer

(∫_^)(3/x*d(x))=3*ln(x)+C

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