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Beliebt Rechnen >

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

Lösung

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

Lösung

ln (2)

+1

Dezimale

0.69314 \dots

Schritte zur Lösung

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

Berechne das unbestimmte Integral:

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

Berechne die Grenzen:

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

= 0 - (- ln (2))

Vereinfache

= ln (2)

Beliebte Beispiele

integral from 0 to 2 of x^2+x

\int_{0}^{2} x^{2} + x d x

integral from 1 to 8 of (8x)/(x^2+6)

\int_{1}^{8} \frac{8 x}{x ^{2} + 6} d x

integral from-pi to 0 of-1cos(nx)

\int_{- π}^{0} - 1 cos (n x) d x

integral from 0 to y of 1/x

\int_{0}^{y} \frac{1}{x} d x

integral from 2 to 3 of 3e^x

\int_{2}^{3} 3 e^{x} d x