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Beliebt Rechnen >

integral from 8 to 11 of 2arccot(x)

Lösung

\int_{8}^{11} 2 arccot (x) d x

Lösung

22 arccot (11) - 16 arccot (8) + ln (122) - ln (65)

+1

Dezimale

0.63447 \dots

Schritte zur Lösung

\int_{8}^{11} 2 arccot (x) d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int_{8}^{11} arccot (x) d x

Wende die partielle Integration an

= 2 [x arccot (x) - \int - \frac{x}{x ^{2} + 1} d x]_{8}^{11}

\int - \frac{x}{x ^{2} + 1} d x = - \frac{1}{2} ln x^{2} + 1

= 2 [x arccot (x) - (- \frac{1}{2} ln x^{2} + 1)]_{8}^{11}

Vereinfache

= 2 [x arccot (x) + \frac{1}{2} ln x^{2} + 1]_{8}^{11}

Berechne die Grenzen:

11 arccot (11) - 8 arccot (8) + \frac{ln ( 122 ) - ln ( 65 )}{2}

= 2 (11 arccot (11) - 8 arccot (8) + \frac{ln ( 122 ) - ln ( 65 )}{2})

Vereinfache

= 22 arccot (11) - 16 arccot (8) + ln (122) - ln (65)

Graph

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