integral from 1 to 3 of 3x(x^2-5)^5

Lösung

\int_{1}^{3} 3 x (x^{2} - 5)^{5} d x

0

Schritte zur Lösung

\int_{1}^{3} 3 x (x^{2} - 5)^{5} d x

Entferne die Konstante:

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

= 3 \cdot \int_{1}^{3} x (x^{2} - 5)^{5} d x

Wende U-Substitution an

= 3 \cdot \int_{- 4}^{4} \frac{u ^{5}}{2} d u

Entferne die Konstante:

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

= 3 \cdot \frac{1}{2} \cdot \int_{- 4}^{4} u^{5} d u

Wende die Potenzregel an

= 3 \cdot \frac{1}{2} [\frac{u ^{6}}{6}]_{- 4}^{4}

Vereinfache

3 \cdot \frac{1}{2} [\frac{u ^{6}}{6}]_{- 4}^{4} : \frac{3}{2} [\frac{u ^{6}}{6}]_{- 4}^{4}

= \frac{3}{2} [\frac{u ^{6}}{6}]_{- 4}^{4}

Berechne die Grenzen:

0

= \frac{3}{2} \cdot 0

Vereinfache

= 0

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