integral from 1 to 3 of x/(3x^2+1)

Lösung

\int_{1}^{3} \frac{x}{3 x ^{2} + 1} d x

\frac{1}{6} ln (7)

Dezimale

0.32431 \dots

Schritte zur Lösung

\int_{1}^{3} \frac{x}{3 x ^{2} + 1} d x

Wende U-Substitution an

= \int_{4}^{28} \frac{1}{6 u} d u

Entferne die Konstante:

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

= \frac{1}{6} \cdot \int_{4}^{28} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{6} [ln ∣ u ∣]_{4}^{28}

Berechne die Grenzen:

ln (28) - 2 ln (2)

= \frac{1}{6} (ln (28) - 2 ln (2))

Vereinfache

= \frac{1}{6} ln (7)

\int_{0}^{2} - 5 x^{2} d x

\int_{0}^{\frac{7}{2}} 7 x - 2 x^{2} d x

\int_{0}^{1} \frac{7}{( 3 x + 4 ) ( 5 x + 2 )} d x

\int_{0}^{8} \frac{1}{x ^{\frac{2}{3}}} d x

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