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

Lösung

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

\frac{2}{5}

Dezimale

0.4

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{1}^{5} \frac{1}{2 u ^{2}} 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}^{5} \frac{1}{u ^{2}} d u

Wende die Potenzregel an

= \frac{1}{2} [- \frac{1}{u}]_{1}^{5}

Berechne die Grenzen:

\frac{4}{5}

= \frac{1}{2} \cdot \frac{4}{5}

Vereinfache

= \frac{2}{5}

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