de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of 64x^3(4x^2+1)^3

Lösung

\int 64 x^{3} (4 x^{2} + 1)^{3} d x

Lösung

64 (\frac{32 x ^{10}}{5} + 6 x^{8} + 2 x^{6} + \frac{x ^{4}}{4}) + C

Schritte zur Lösung

\int 64 x^{3} (4 x^{2} + 1)^{3} d x

Entferne die Konstante:

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

= 64 \cdot \int x^{3} (4 x^{2} + 1)^{3} d x

Multipliziere aus

x^{3} (4 x^{2} + 1)^{3} : 64 x^{9} + 48 x^{7} + 12 x^{5} + x^{3}

= 64 \cdot \int 64 x^{9} + 48 x^{7} + 12 x^{5} + x^{3} 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

= 64 (\int 64 x^{9} d x + \int 48 x^{7} d x + \int 12 x^{5} d x + \int x^{3} d x)

\int 64 x^{9} d x = \frac{32 x ^{10}}{5}

\int 48 x^{7} d x = 6 x^{8}

\int 12 x^{5} d x = 2 x^{6}

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

= 64 (\frac{32 x ^{10}}{5} + 6 x^{8} + 2 x^{6} + \frac{x ^{4}}{4})

Füge eine Konstante zur Lösung hinzu

= 64 (\frac{32 x ^{10}}{5} + 6 x^{8} + 2 x^{6} + \frac{x ^{4}}{4}) + C

Graph

Beliebte Beispiele

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

derivative of (cot^2(2x)/(1+x^2))

derivative 2x(x+5)

d/(dt)(6cos^3(t))

integral of ((3x^3-5x^2+10x-3))/(3x+1)