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

Lösung

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

- \frac{3}{20}

Dezimale

- 0.15

Schritte zur Lösung

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

Wende U-Substitution an

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

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

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

Wende die Potenzregel an

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

Berechne die Grenzen:

\frac{3}{10}

= - \frac{1}{2} \cdot \frac{3}{10}

Vereinfache

= - \frac{3}{20}

\int_{1}^{10} \frac{2 x ( x - 1 )}{81} d x

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