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

Lösung

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

\frac{243}{10}

Dezimale

24.3

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{0}^{3} \frac{u ^{4}}{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_{0}^{3} u^{4} d u

Wende die Potenzregel an

= \frac{1}{2} [\frac{u ^{5}}{5}]_{0}^{3}

Berechne die Grenzen:

\frac{243}{5}

= \frac{1}{2} \cdot \frac{243}{5}

Vereinfache

= \frac{243}{10}

\int_{0}^{\frac{π}{6}} sin (6 x) d x

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