integral from 0 to 1 of x^8(1+x^9)^8

Lösung

\int_{0}^{1} x^{8} (1 + x^{9})^{8} d x

\frac{511}{81}

Dezimale

6.30864 \dots

Schritte zur Lösung

\int_{0}^{1} x^{8} (1 + x^{9})^{8} d x

Wende U-Substitution an

= \int_{1}^{2} \frac{u ^{8}}{9} d u

Entferne die Konstante:

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

= \frac{1}{9} \cdot \int_{1}^{2} u^{8} d u

Wende die Potenzregel an

= \frac{1}{9} [\frac{u ^{9}}{9}]_{1}^{2}

Berechne die Grenzen:

\frac{511}{9}

= \frac{1}{9} \cdot \frac{511}{9}

Vereinfache

= \frac{511}{81}

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