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Beliebt Rechnen >

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

Lösung

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

Lösung

ln (2)

+1

Dezimale

0.69314 \dots

Schritte zur Lösung

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

= 0 - (- ln (2))

Vereinfache

= ln (2)

Beliebte Beispiele

derivative of 2^xln^2(2)

\frac{d}{d x} (2^{x} ln^{2} (2))

fläche 9x+11,7x+14,[23,13]

a re a 9 x + 11, 7 x + 14, [23, 13]

(\partial)/(\partial y)(e^ysin(x))

\frac{\partial}{\partial y} (e^{y} sin (x))

(d^2)/(dx^2)(x\sqrt[3]{x})

\frac{d ^{2}}{d x ^{2}} (x 3 x)

inverselaplace ((4s-18))/(s^2-6s+10)

in v erse l a pl a ce \frac{( 4 s - 18 )}{s ^{2} - 6 s + 10}