Evaluate the Integral integral of 5/x with respect to x

Problem

(∫_^)(5/x*d(x))

Solution

1. Identify the constant factor in the integrand. The expression 5/x can be written as 5⋅1/x

2. Apply the constant multiple rule for integration, which allows the constant 5 to be moved outside the integral sign.

(∫_^)(5/x*d(x))=5*(∫_^)(1/x*d(x))

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

5*(∫_^)(1/x*d(x))=5*ln(x)+C

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

Final Answer

(∫_^)(5/x*d(x))=5*ln(x)+C

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