Beliebt >

integral from 0 to 5 of x/(3x^2+6)

Lösung

\int_{0}^{5} \frac{x}{3 x ^{2} + 6} d x

\frac{1}{6} ln (\frac{27}{2})

Dezimale Notation

0.43378 \dots

Schritte zur Lösung

\int_{0}^{5} \frac{x}{3 x ^{2} + 6} d x

Wende U-Substitution an

: \int_{6}^{81} \frac{1}{6 u} d u

= \int_{6}^{81} \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_{6}^{81} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{6} [ln ∣ u ∣]_{6}^{81}

Berechne die Grenzen:

4 ln (3) - ln (6)

= \frac{1}{6} (4 ln (3) - ln (6))

Vereinfache

= \frac{1}{6} ln (\frac{27}{2})

\int_{0}^{\frac{π}{3}} (sin (x)) d x

\int_{0}^{1} sin (y^{2}) d y

\int_{0}^{π} 2 x cos (n x) d x

\int_{0}^{9} 2 x d x

\int_{0}^{4} (6 x^{3} - 3 x) d x