integral from 0 to infinity of x/(3+x^4)

Lösung

\int_{0}^{\infty} \frac{x}{3 + x ^{4}} d x

\frac{π}{4 3}

Dezimale

0.45344 \dots

Schritte zur Lösung

\int_{0}^{\infty} \frac{x}{3 + x ^{4}} d x

Berechne das unbestimmte Integral:

\int \frac{x}{3 + x ^{4}} d x = \frac{1}{2 3} arctan (\frac{x ^{2}}{3}) + C

Berechne die Grenzen:

\int_{0}^{\infty} \frac{x}{3 + x ^{4}} d x = \frac{π}{4 3} - 0

= \frac{π}{4 3} - 0

Vereinfache

= \frac{π}{4 3}

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