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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{3}{16}

+1

Dezimale

0.1875

Schritte zur Lösung

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

Wende U-Substitution an

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

Entferne die Konstante:

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

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

Wende die Potenzregel an

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

Berechne die Grenzen:

\frac{3}{8}

= \frac{1}{2} \cdot \frac{3}{8}

Vereinfache

= \frac{3}{16}

Graph

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