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Calculus · Definite-Integrals

Integrate 1/x from 1 to oo

\int_{1}^{\infty} \frac{1}{x}\, dx

Step by step

  1. \int_{1}^{\infty} \frac{1}{x}\, dx

    First find an antiderivative F, then evaluate F(b) − F(a).

  2. \int \frac{1}{x}\, dx = \log{\left(x \right)}

    ∫ 1/u du = ln|u|.

  3. F(\infty) - F(1) = \left(\infty\right) - \left(0\right)

    Fundamental theorem of calculus: plug in the limits.

  4. = \infty

    Simplify.

Reveal the answer
\infty