integral from 3 to infinity of 7/(x^2+2)

Lösung

\int_{3}^{\infty} \frac{7}{x ^{2} + 2} d x

\frac{7 π - 14 arctan ( \frac{3 2}{2} )}{2 2}

Dezimale

2.18041 \dots

Schritte zur Lösung

\int_{3}^{\infty} \frac{7}{x ^{2} + 2} d x

Berechne das unbestimmte Integral:

\int \frac{7}{x ^{2} + 2} d x = \frac{7}{2} arctan (\frac{x}{2}) + C

Berechne die Grenzen:

\int_{3}^{\infty} \frac{7}{x ^{2} + 2} d x = \frac{7}{2} \cdot \frac{π}{2} - \frac{7}{2} arctan (\frac{3}{2})

= \frac{7}{2} \cdot \frac{π}{2} - \frac{7}{2} arctan (\frac{3}{2})

Vereinfache

= \frac{7 π - 14 arctan ( \frac{3 2}{2} )}{2 2}

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