Calculus • Step-by-Step

Integral of 1/x dx with Steps

Step-by-step integration of 1/x dx. Explains why the standard power rule fails for n = -1 and proves that the antiderivative equals ln|x| + C.

Problem Statement

\int \frac{1}{x} \, dx

Final Result

F(x) = \ln|x| + C

Formula Required: Logarithmic Integration Rule

The power rule x^(n+1)/(n+1) divides by zero when n = -1. The antiderivative is ln|x|.

\int \frac{1}{x} \, dx = \ln|x| + C

Step-by-Step Solution

2 Steps

Set up the indefinite integral with respect to variable $x$.

\int \left( \frac{1}{x} \right) \, dx

Apply the Logarithmic Integration Rule to find the antiderivative.

F(x) = \ln|x|

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Common Questions About Integral of 1/x dx

Why do we need the absolute value in ln|x| + C?

Because the natural logarithm is only defined for positive numbers, but 1/x exists for negative numbers too. The absolute value extends the domain to all x ≠ 0.