de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (4x^3-2)2x^2

Lösung

\int (4 x^{3} - 2) 2 x^{2} d x

Lösung

4 (\frac{x ^{6}}{3} - \frac{x ^{3}}{3}) + C

Schritte zur Lösung

\int (4 x^{3} - 2) \cdot 2 x^{2} d x

Entferne die Konstante:

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

= 2 \cdot \int (4 x^{3} - 2) x^{2} d x

(4 x^{3} - 2) x^{2} = 2 (2 x^{3} - 1) x^{2}

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

Entferne die Konstante:

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

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

Multipliziere aus

(2 x^{3} - 1) x^{2} : 2 x^{5} - x^{2}

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

\int 2 x^{5} d x = \frac{x ^{6}}{3}

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

= 2 \cdot 2 (\frac{x ^{6}}{3} - \frac{x ^{3}}{3})

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of x*arctan(sqrt(x^2-1))

\int x \cdot arctan (x^{2} - 1) d x

integral of x^2(3-10x^3)^4

\int x^{2} (3 - 10 x^{3})^{4} d x

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

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

integral of (e^x)/((9-e^x)^2)

\int \frac{e ^{x}}{( 9 - e ^{x} ) ^{2}} d x

integral of-4/(x(ln(x))^4)

\int - \frac{4}{x ( ln ( x ) ) ^{4}} d x