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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{1}{12}

+1

Dezimale

0.08333 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= 2 \cdot \int_{3}^{4} \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_{3}^{4} \frac{1}{u ^{2}} d u

Wende die Potenzregel an

= 2 \cdot \frac{1}{2} [- \frac{1}{u}]_{3}^{4}

Vereinfache

2 \cdot \frac{1}{2} [- \frac{1}{u}]_{3}^{4} : [- \frac{1}{u}]_{3}^{4}

= [- \frac{1}{u}]_{3}^{4}

Berechne die Grenzen:

\frac{1}{12}

= \frac{1}{12}

Graph

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