de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral from 1 to 3 of (2x)/((x^2+4)^2)

Lösung

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

Lösung

\frac{8}{65}

+1

Dezimale

0.12307 \dots

Schritte zur Lösung

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

Entferne die Konstante:

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

= 2 \cdot \int_{1}^{3} \frac{x}{( x ^{2} + 4 ) ^{2}} d x

Wende U-Substitution an

= 2 \cdot \int_{5}^{13} \frac{1}{2 u ^{2}} d u

Entferne die Konstante:

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

= 2 \cdot \frac{1}{2} \cdot \int_{5}^{13} \frac{1}{u ^{2}} d u

Wende die Potenzregel an

= 2 \cdot \frac{1}{2} [- \frac{1}{u}]_{5}^{13}

Vereinfache

2 \cdot \frac{1}{2} [- \frac{1}{u}]_{5}^{13} : [- \frac{1}{u}]_{5}^{13}

= [- \frac{1}{u}]_{5}^{13}

Berechne die Grenzen:

\frac{8}{65}

= \frac{8}{65}

Graph

Beliebte Beispiele

integral from 0 to 1/2 of e^{2x}

\int_{0}^{\frac{1}{2}} e^{2 x} d x

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

\int_{- 2}^{2} (x - 5) d x

integral from 5 to 10 of (6x)/(3x^2-5)

\int_{5}^{10} \frac{6 x}{3 x ^{2} - 5} d x

integral from-3 to-1 of x

\int_{- 3}^{- 1} x d x

integral from 4 to 9 of x^2

\int_{4}^{9} x^{2} d x