Evaluate the Integral integral of 5x^-1 with respect to x

Problem

(∫_^)(5*x(−1)*d(x))

Solution

1. Rewrite the expression using the property of exponents where x(−1)=1/x

(∫_^)(5/x*d(x))

2. Factor out the constant coefficient 5 from the integral.

5*(∫_^)(1/x*d(x))

3. Apply the integration rule for the reciprocal function, which states that (∫_^)(1/x*d(x))=ln(x)+C

5*ln(x)+C

Final Answer

(∫_^)(5*x(−1)*d(x))=5*ln(x)+C

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