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Beliebt Rechnen >

integral of 60x^2(1-4x^3)^4

Lösung

\int 60 x^{2} (1 - 4 x^{3})^{4} d x

Lösung

60 (\frac{x ^{3}}{3} - \frac{8 x ^{6}}{3} + \frac{32 x ^{9}}{3} - \frac{64 x ^{12}}{3} + \frac{256 x ^{15}}{15}) + C

Schritte zur Lösung

\int 60 x^{2} (1 - 4 x^{3})^{4} d x

Entferne die Konstante:

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

= 60 \cdot \int x^{2} (1 - 4 x^{3})^{4} d x

Faktorisiere

1 - 4 x^{3} : - (- 1 + 4 x^{3})

= 60 \cdot \int x^{2} (- (- 1 + 4 x^{3}))^{4} d x

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

= 60 \cdot \int x^{2} (- 1 + 4 x^{3})^{4} d x

Multipliziere aus

x^{2} (- 1 + 4 x^{3})^{4} : x^{2} - 16 x^{5} + 96 x^{8} - 256 x^{11} + 256 x^{14}

= 60 \cdot \int x^{2} - 16 x^{5} + 96 x^{8} - 256 x^{11} + 256 x^{14} 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

= 60 (\int x^{2} d x - \int 16 x^{5} d x + \int 96 x^{8} d x - \int 256 x^{11} d x + \int 256 x^{14} d x)

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

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

\int 96 x^{8} d x = \frac{32 x ^{9}}{3}

\int 256 x^{11} d x = \frac{64 x ^{12}}{3}

\int 256 x^{14} d x = \frac{256 x ^{15}}{15}

= 60 (\frac{x ^{3}}{3} - \frac{8 x ^{6}}{3} + \frac{32 x ^{9}}{3} - \frac{64 x ^{12}}{3} + \frac{256 x ^{15}}{15})

Füge eine Konstante zur Lösung hinzu

= 60 (\frac{x ^{3}}{3} - \frac{8 x ^{6}}{3} + \frac{32 x ^{9}}{3} - \frac{64 x ^{12}}{3} + \frac{256 x ^{15}}{15}) + C

Graph

Beliebte Beispiele

derivative f(x)=\sqrt[3]{e^{2x}+x^3}

d er i v a t i v e f (x) = 3 e^{2 x} + x^{3}

derivative f(x)=x^{5/6}

d er i v a t i v e f (x) = x^{\frac{5}{6}}

tangent y=10-3x-x^2

t an g e n t y = 10 - 3 x - x^{2}

(dy)/(dx)+ycos(x)=4cos(x),y(0)=6

\frac{d y}{d x} + y cos (x) = 4 cos (x), y (0) = 6

integral of 3xsqrt(4-x^2)

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