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Beliebt Rechnen >

integral from 0 to 1 of (2x)/((x^2+2)^3)

Lösung

\int_{0}^{1} \frac{2 x}{( x ^{2} + 2 ) ^{3}} d x

Lösung

\frac{5}{72}

+1

Dezimale

0.06944 \dots

Schritte zur Lösung

\int_{0}^{1} \frac{2 x}{( x ^{2} + 2 ) ^{3}} d x

Entferne die Konstante:

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

= 2 \cdot \int_{0}^{1} \frac{x}{( x ^{2} + 2 ) ^{3}} d x

Wende U-Substitution an

= 2 \cdot \int_{2}^{3} \frac{1}{2 u ^{3}} 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_{2}^{3} \frac{1}{u ^{3}} d u

Wende die Potenzregel an

= 2 \cdot \frac{1}{2} [- \frac{1}{2 u ^{2}}]_{2}^{3}

Vereinfache

2 \cdot \frac{1}{2} [- \frac{1}{2 u ^{2}}]_{2}^{3} : [- \frac{1}{2 u ^{2}}]_{2}^{3}

= [- \frac{1}{2 u ^{2}}]_{2}^{3}

Berechne die Grenzen:

\frac{5}{72}

= \frac{5}{72}

Graph

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