CalcRef

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.

Worked examples

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

Answer: 1

Find ∫ 3/x dx.
  1. 3 ∫ 1/x dx = 3 ln|x| + C

Answer: 3 ln|x| + C

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