Understanding the Integral of 1/x with Respect to x | A Comprehensive Explanation with the Power Rule

∫1/xdx=

The expression ∫ 1/x dx represents the integral of the function 1/x with respect to the variable x

The expression ∫ 1/x dx represents the integral of the function 1/x with respect to the variable x.

To evaluate this integral, we can use the properties of logarithms. The integral ∫ 1/x dx can be rewritten as ∫ x^(-1) dx.

Using the power rule for integrals, we have:

∫ x^(-1) dx = ln|x| + C

Where ln(x) is the natural logarithm function and C is the constant of integration.

Therefore, the integral of 1/x with respect to x is ln|x| + C.

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