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The integral of 1/x dx is ln|x| + C, where C is the constant of integration.

To evaluate the integral of 1/x dx, we can use the formula for the natural logarithm: ln(x) = ∫(1/x) dx. We can rewrite the integral as ∫(1/x) dx = ln|x| + C, where C is the constant of integration.

To see why this is true, we can differentiate ln|x| + C with respect to x. Using the chain rule, we have d/dx ln|x| = 1/x, so the derivative of ln|x| + C is indeed 1/x.

Therefore, the integral of 1/x dx is ln|x| + C, where C is the constant of integration. Note that the absolute value of x is necessary because ln(x) is undefined for x ≤ 0.

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