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Calculus · Definite-Integrals

Integrate 1/(x^2 + 4) from -oo to oo

\int_{-\infty}^{\infty} \frac{1}{x^{2} + 4}\, dx

Step by step

  1. \int_{-\infty}^{\infty} \frac{1}{x^{2} + 4}\, dx

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

  2. \int \frac{1}{x^{2} + 4}\, dx = \frac{\operatorname{atan}{\left(\frac{x}{2} \right)}}{2}

    Recognise an inverse-trig / inverse-hyperbolic form.

  3. F(\infty) - F(-\infty) = \left(\frac{\pi}{4}\right) - \left(- \frac{\pi}{4}\right)

    Fundamental theorem of calculus: plug in the limits.

  4. = \frac{\pi}{2} \approx 1.5708

    Simplify.

Reveal the answer
\frac{\pi}{2}