integral from 1 to 2 of x/((x^2+4)^3)

Lösung

\int_{1}^{2} \frac{x}{( x ^{2} + 4 ) ^{3}} d x

\frac{39}{6400}

Dezimale

0.00609375

Schritte zur Lösung

\int_{1}^{2} \frac{x}{( x ^{2} + 4 ) ^{3}} d x

Wende U-Substitution an

= \int_{5}^{8} \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_{5}^{8} \frac{1}{u ^{3}} d u

Wende die Potenzregel an

= \frac{1}{2} [- \frac{1}{2 u ^{2}}]_{5}^{8}

Berechne die Grenzen:

\frac{39}{3200}

= \frac{1}{2} \cdot \frac{39}{3200}

Vereinfache

= \frac{39}{6400}

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