integral from 0 to 1 of (1+5x)^3

Lösung

\int_{0}^{1} (1 + 5 x)^{3} d x

\frac{259}{4}

Dezimale

64.75

Schritte zur Lösung

\int_{0}^{1} (1 + 5 x)^{3} d x

Wende U-Substitution an

= \int_{1}^{6} \frac{u ^{3}}{5} d u

Entferne die Konstante:

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

= \frac{1}{5} \cdot \int_{1}^{6} u^{3} d u

Wende die Potenzregel an

= \frac{1}{5} [\frac{u ^{4}}{4}]_{1}^{6}

Berechne die Grenzen:

\frac{1295}{4}

= \frac{1}{5} \cdot \frac{1295}{4}

Vereinfache

= \frac{259}{4}

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