de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of 8x(4x^2+4)^2

Lösung

\int 8 x (4 x^{2} + 4)^{2} d x

Lösung

8 (\frac{8 x ^{6}}{3} + 8 x^{4} + 8 x^{2}) + C

Schritte zur Lösung

\int 8 x (4 x^{2} + 4)^{2} d x

Entferne die Konstante:

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

= 8 \cdot \int x (4 x^{2} + 4)^{2} d x

Multipliziere aus

x (4 x^{2} + 4)^{2} : 16 x^{5} + 32 x^{3} + 16 x

= 8 \cdot \int 16 x^{5} + 32 x^{3} + 16 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

= 8 (\int 16 x^{5} d x + \int 32 x^{3} d x + \int 16 x d x)

\int 16 x^{5} d x = \frac{8 x ^{6}}{3}

\int 32 x^{3} d x = 8 x^{4}

\int 16 x d x = 8 x^{2}

= 8 (\frac{8 x ^{6}}{3} + 8 x^{4} + 8 x^{2})

Füge eine Konstante zur Lösung hinzu

= 8 (\frac{8 x ^{6}}{3} + 8 x^{4} + 8 x^{2}) + C

Graph

Beliebte Beispiele

integral of t^2+t-2

\int t^{2} + t - 2 d t

integral of x*e^{-2}

\int x \cdot e^{- 2} d x

integral of x^3(3x^4+2)^6

\int x^{3} (3 x^{4} + 2)^{6} d x

integral of (-4)/(sqrt(x+1)+\sqrt{x)}

\int \frac{- 4}{x + 1 + x} d x

integral of x^3sqrt(a+bx^4)

\int x^{3} a + b x^{4} d x