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Beliebt Rechnen >

integral of (x^2-5)^20.2x

Lösung

\int (x^{2} - 5)^{2} 0.2 x d x

Lösung

0.2 (0.16666 \dots x^{6} - 2.5 x^{4} + 12.5 x^{2}) + C

Schritte zur Lösung

\int (x^{2} - 5)^{2} \cdot 0.2 x d x

Entferne die Konstante:

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

= 0.2 \cdot \int (x^{2} - 5)^{2} x d x

Multipliziere aus

(x^{2} - 5)^{2} x : x^{5} - 10 x^{3} + 25 x

= 0.2 \cdot \int x^{5} - 10 x^{3} + 25 x d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 0.2 (\int x^{5} d x - \int 10 x^{3} d x + \int 25 x d x)

\int x^{5} d x = \frac{x ^{6}}{6}

\int 10 x^{3} d x = \frac{5 x ^{4}}{2}

\int 25 x d x = \frac{25 x ^{2}}{2}

= 0.2 (\frac{x ^{6}}{6} - \frac{5 x ^{4}}{2} + \frac{25 x ^{2}}{2})

Vereinfache

= 0.2 (0.16666 \dots x^{6} - 2.5 x^{4} + 12.5 x^{2})

Füge eine Konstante zur Lösung hinzu

= 0.2 (0.16666 \dots x^{6} - 2.5 x^{4} + 12.5 x^{2}) + C

Graph

Beliebte Beispiele

integral from 6 to 7 of x/(x-6)

\int_{6}^{7} \frac{x}{x - 6} d x

integral of (3x+2)

\int (3 x + 2) d x

integral of-1e^x

\int - 1 e^{x} d x

integral of (x^3)/3+2x-5

\int \frac{x ^{3}}{3} + 2 x - 5 d x

limit as x approaches 3-of 2x^3

x \to 3 - lim (2 x^{3})