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Beliebt Rechnen >

integral from 8 to infinity of 1/(x^2+x)

Lösung

\int_{8}^{\infty} \frac{1}{x ^{2} + x} d x

Lösung

- (3 ln (2) - 2 ln (3))

+1

Dezimale

0.11778 \dots

Schritte zur Lösung

\int_{8}^{\infty} \frac{1}{x ^{2} + x} d x

Berechne das unbestimmte Integral:

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

Berechne die Grenzen:

\int_{8}^{\infty} \frac{1}{x ^{2} + x} d x = 0 - (3 ln (2) - 2 ln (3))

= 0 - (3 ln (2) - 2 ln (3))

Vereinfache

= - (3 ln (2) - 2 ln (3))

Beliebte Beispiele

y^{^{'}} = (y + 4 x)^{2}

limit as x approaches 1+of (x^2)/(x^2-1)

x \to 1 + lim (\frac{x ^{2}}{x ^{2} - 1})

(dy)/(dx)=3e^{2x}y^2

\frac{d y}{d x} = 3 e^{2 x} y^{2}

integral of x^35^{-x}

\int x^{3} 5^{- x} d x

integral from 0 to 1 of e^{(2x)/3}

\int_{0}^{1} e^{\frac{2 x}{3}} d x