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Integrals · Basic Antiderivatives

Integral of 1/x

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

The antiderivative of 1/x is the natural logarithm of the absolute value of x.

Conditions. x ≠ 0.
  • 2 worked examples
  • 19 in Integrals

Worked examples

Find ∫₁ᵉ (1/x) dx.
  1. [ln|x|]₁ᵉ = ln e - ln 1 = 1 - 0

Answer: 1

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Find ∫ 3/x dx.

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Common questions

What is the Integral of 1/x?

The antiderivative of 1/x is the natural logarithm of the absolute value of x. It is one of the integrals formulas in the CalcRef reference.

When does the Integral of 1/x apply?

The Integral of 1/x holds under this condition: x ≠ 0.

How do you use the Integral of 1/x?

Worked example. Find ∫₁ᵉ (1/x) dx. [ln|x|]₁ᵉ = ln e - ln 1 = 1 - 0. Answer: 1.

Practice

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