integral from 0 to 1 of x/(1+5x^2)

Lösung

\int_{0}^{1} \frac{x}{1 + 5 x ^{2}} d x

\frac{1}{10} ln (6)

Dezimale

0.17917 \dots

Schritte zur Lösung

\int_{0}^{1} \frac{x}{1 + 5 x ^{2}} d x

Wende U-Substitution an

= \int_{1}^{6} \frac{1}{10 u} d u

Entferne die Konstante:

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

= \frac{1}{10} \cdot \int_{1}^{6} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{10} [ln ∣ u ∣]_{1}^{6}

Berechne die Grenzen:

ln (6)

= \frac{1}{10} ln (6)

\int_{0}^{1} \frac{10}{1 + x ^{2}} d x

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