de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (x^2-3)^2(2x)

Lösung

\int (x^{2} - 3)^{2} (2 x) d x

Lösung

\frac{x ^{6}}{3} - 3 x^{4} + 9 x^{2} + C

Schritte zur Lösung

\int (x^{2} - 3)^{2} \cdot 2 x d x

Entferne die Konstante:

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

= 2 \cdot \int (x^{2} - 3)^{2} x d x

Multipliziere aus

(x^{2} - 3)^{2} x : x^{5} - 6 x^{3} + 9 x

= 2 \cdot \int x^{5} - 6 x^{3} + 9 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

= 2 (\int x^{5} d x - \int 6 x^{3} d x + \int 9 x d x)

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

\int 6 x^{3} d x = \frac{3 x ^{4}}{2}

\int 9 x d x = \frac{9 x ^{2}}{2}

= 2 (\frac{x ^{6}}{6} - \frac{3 x ^{4}}{2} + \frac{9 x ^{2}}{2})

Vereinfache

2 (\frac{x ^{6}}{6} - \frac{3 x ^{4}}{2} + \frac{9 x ^{2}}{2}) : \frac{x ^{6}}{3} - 3 x^{4} + 9 x^{2}

= \frac{x ^{6}}{3} - 3 x^{4} + 9 x^{2}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{6}}{3} - 3 x^{4} + 9 x^{2} + C

Graph

Beliebte Beispiele

limit as x approaches 0+of 1/(3x)

x \to 0 + lim (\frac{1}{3 x})

integral of 9/(x^2+9)

\int \frac{9}{x ^{2} + 9} d x

integral of 1/(9-6x)

\int \frac{1}{9 - 6 x} d x

integral of 1/(e^x-1)

\int \frac{1}{e ^{x} - 1} d x

integral of sin(x/2)

\int sin (\frac{x}{2}) d x