de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{1}{3} ln (\frac{18}{7})

+1

Dezimale

0.31482 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{14}^{36} \frac{1}{3 u} d u

Entferne die Konstante:

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

= \frac{1}{3} \cdot \int_{14}^{36} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{3} [ln ∣ u ∣]_{14}^{36}

Berechne die Grenzen:

2 ln (6) - ln (14)

= \frac{1}{3} (2 ln (6) - ln (14))

Vereinfache

= \frac{1}{3} ln (\frac{18}{7})

Graph

Beliebte Beispiele

integral from 0 to 5 of x/(x-2)

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

integral of 3xsec^2(4)x^2

\int 3 x sec^{2} (4) x^{2} d x

\frac{d x}{d t} = r x

derivative sqrt(35x)ln(10x)

d er i v a t i v e 35 x ln (10 x)

(1+x^4)dy+x(1+4y^2)dx=0,y(1)=0

(1 + x^{4}) d y + x (1 + 4 y^{2}) d x = 0, y (1) = 0