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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{1}{9}

+1

Dezimale

0.11111 \dots

Schritte zur Lösung

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

Wende U-Substitution an

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

Entferne die Konstante:

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

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

Wende die Potenzregel an

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

Berechne die Grenzen:

\frac{4}{9}

= \frac{1}{4} \cdot \frac{4}{9}

Vereinfache

= \frac{1}{9}

Graph

Beliebte Beispiele

integral from 0 to 3 of 1/(x-3)

\int_{0}^{3} \frac{1}{x - 3} d x

integral from 0 to 1 of 5x^4

\int_{0}^{1} 5 x^{4} d x

integral from 1 to 2 of 15x^2(x^3-7)^4

\int_{1}^{2} 15 x^{2} (x^{3} - 7)^{4} d x

integral from 0 to 10 of 4x

\int_{0}^{10} 4 x d x

integral from 0 to 4 of 2e^x

\int_{0}^{4} 2 e^{x} d x