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Beliebt Rechnen >

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

Lösung

\int_{0}^{2} \frac{2 x}{( x ^{2} + 5 ) ^{2}} d x

Lösung

\frac{4}{45}

+1

Dezimale

0.08888 \dots

Schritte zur Lösung

\int_{0}^{2} \frac{2 x}{( x ^{2} + 5 ) ^{2}} d x

Entferne die Konstante:

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

= 2 \cdot \int_{0}^{2} \frac{x}{( x ^{2} + 5 ) ^{2}} d x

Wende U-Substitution an

= 2 \cdot \int_{5}^{9} \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}^{9} \frac{1}{u ^{2}} d u

Wende die Potenzregel an

= 2 \cdot \frac{1}{2} [- \frac{1}{u}]_{5}^{9}

Vereinfache

2 \cdot \frac{1}{2} [- \frac{1}{u}]_{5}^{9} : [- \frac{1}{u}]_{5}^{9}

= [- \frac{1}{u}]_{5}^{9}

Berechne die Grenzen:

\frac{4}{45}

= \frac{4}{45}

Graph

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