Evaluate the Integral integral of 1/(x-3) with respect to x

Problem

(∫_^)(1/(x−3)*d(x))

Solution

1. Identify the form of the integrand, which is a rational function where the numerator is the derivative of the denominator.

2. Apply the rule for the integral of the reciprocal function, (∫_^)(1/u*d(u))=ln(u)+C

3. Substitute u=x−3 Since the derivative of x−3 is 1 the integral follows the natural logarithm form directly.

4. Add the constant of integration C to complete the indefinite integral.

Final Answer

(∫_^)(1/(x−3)*d(x))=ln(x−3)+C

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