Evaluate the Integral integral of 1/x with respect to x

Problem

${\int }_{}^{}\frac{1}{x}dx$

Solution

1. Identify the standard integral form for the reciprocal function.

2. Apply the rule for the integral of $\frac{1}{x}$ which states that the antiderivative is the natural logarithm of the absolute value of $x$

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

Final Answer

${\int }_{}^{}\frac{1}{x}dx=\ln x+C$

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