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Beliebt Rechnen >

integral from 3 to 5 of x/(x^2-2)

Lösung

\int_{3}^{5} \frac{x}{x ^{2} - 2} d x

Lösung

\frac{1}{2} (ln (23) - ln (7))

+1

Dezimale

0.59479 \dots

Schritte zur Lösung

\int_{3}^{5} \frac{x}{x ^{2} - 2} d x

Wende U-Substitution an

= \int_{7}^{23} \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_{7}^{23} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{2} [ln ∣ u ∣]_{7}^{23}

Berechne die Grenzen:

ln (23) - ln (7)

= \frac{1}{2} (ln (23) - ln (7))

Graph

Beliebte Beispiele

integral of (2x+2)/(x^2+2x-1)

\int \frac{2 x + 2}{x ^{2} + 2 x - 1} d x

integral of 4x^2sin(pix)

\int 4 x^{2} sin (π x) d x

(\partial)/(\partial x)(ln(2x^2y))

\frac{\partial}{\partial x} (ln (2 x^{2} y))

integral of 2/(1+x^2)-4/x

\int \frac{2}{1 + x ^{2}} - \frac{4}{x} d x

derivative y=sqrt(25-x^2)

d er i v a t i v e y = 25 - x^{2}