integral from 1 to infinity of x/(x^4+1)

Lösung

\int_{1}^{\infty} \frac{x}{x ^{4} + 1} d x

\frac{π}{8}

Dezimale

0.39269 \dots

Schritte zur Lösung

\int_{1}^{\infty} \frac{x}{x ^{4} + 1} d x

Berechne das unbestimmte Integral:

\int \frac{x}{x ^{4} + 1} d x = \frac{1}{2} arctan (x^{2}) + C

Berechne die Grenzen:

\int_{1}^{\infty} \frac{x}{x ^{4} + 1} d x = \frac{π}{4} - \frac{π}{8}

= \frac{π}{4} - \frac{π}{8}

Vereinfache

= \frac{π}{8}

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