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

Lösung

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

\frac{1}{3}

Dezimale

0.33333 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= 2 \cdot \int_{2}^{6} \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_{2}^{6} \frac{1}{u ^{2}} d u

Wende die Potenzregel an

= 2 \cdot \frac{1}{2} [- \frac{1}{u}]_{2}^{6}

Vereinfache

2 \cdot \frac{1}{2} [- \frac{1}{u}]_{2}^{6} : [- \frac{1}{u}]_{2}^{6}

= [- \frac{1}{u}]_{2}^{6}

Berechne die Grenzen:

\frac{1}{3}

= \frac{1}{3}

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