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Beliebt Rechnen >

integral from 0 to 2 of x/(x^2+1)

Lösung

\int_{0}^{2} \frac{x}{x ^{2} + 1} d x

Lösung

\frac{1}{2} ln (5)

+1

Dezimale

0.80471 \dots

Schritte zur Lösung

\int_{0}^{2} \frac{x}{x ^{2} + 1} d x

Wende U-Substitution an

= \int_{1}^{5} \frac{1}{2 u} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{1}^{5} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{2} [ln ∣ u ∣]_{1}^{5}

Berechne die Grenzen:

ln (5)

= \frac{1}{2} ln (5)

Graph

Beliebte Beispiele

(y/2+2x)dx+(-1)dy=0

(\frac{y}{2} + 2 x) d x + (- 1) d y = 0

(xdy)/(dx)+xy=1-y

\frac{x d y}{d x} + x y = 1 - y

\frac{d y}{d x} = - 2 y

sum from n=2 to infinity of ne^{-3n}

n = 2 \sum \infty n e^{- 3 n}

limit as n approaches infinity of 2^{-n}

n \to \infty lim (2^{- n})