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Beliebt Rechnen >

integral from 7 to 8 of x/(x^2-3)

Lösung

\int_{7}^{8} \frac{x}{x ^{2} - 3} d x

Lösung

\frac{1}{2} (ln (61) - ln (46))

+1

Dezimale

0.14111 \dots

Schritte zur Lösung

\int_{7}^{8} \frac{x}{x ^{2} - 3} d x

Wende U-Substitution an

= \int_{46}^{61} \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_{46}^{61} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{2} [ln ∣ u ∣]_{46}^{61}

Berechne die Grenzen:

ln (61) - ln (46)

= \frac{1}{2} (ln (61) - ln (46))

Graph

Beliebte Beispiele

limit as x approaches 7+of 3x+5

x \to 7 + lim (3 x + 5)

derivative sqrt(x)

d er i v a t i v e x

(dy)/(dt)=2y-3e^{-t}

\frac{d y}{d t} = 2 y - 3 e^{- t}

limit as x approaches 0-of-2x^2+7x

x \to 0 - lim (- 2 x^{2} + 7 x)

tangent y=x^4+6x^2-x,(1,6)

t an g e n t y = x^{4} + 6 x^{2} - x, (1, 6)