Evaluate the Integral integral of -5/r with respect to r

Problem

(∫_^)(−5/r*d(r))

Solution

1. Factor out the constant coefficient −5 from the integral to simplify the expression.

(∫_^)(−5/r*d(r))=−5*(∫_^)(1/r*d(r))

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

(∫_^)(1/r*d(r))=ln(r)

3. Combine the results by multiplying the constant back into the antiderivative and adding the constant of integration C

−5*ln(r)+C

Final Answer

(∫_^)(−5/r*d(r))=−5*ln(r)+C

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