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Beliebt Rechnen >

integral of 9x^4(x^5+2)^8

Lösung

\int 9 x^{4} (x^{5} + 2)^{8} d x

Lösung

9 (\frac{x ^{45}}{45} + \frac{2 x ^{40}}{5} + \frac{16 x ^{35}}{5} + \frac{224 x ^{30}}{15} + \frac{224 x ^{25}}{5} + \frac{448 x ^{20}}{5} + \frac{1792 x ^{15}}{15} + \frac{512 x ^{10}}{5} + \frac{256 x ^{5}}{5}) + C

Schritte zur Lösung

\int 9 x^{4} (x^{5} + 2)^{8} d x

Entferne die Konstante:

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

= 9 \cdot \int x^{4} (x^{5} + 2)^{8} d x

Multipliziere aus

x^{4} (x^{5} + 2)^{8} : x^{44} + 16 x^{39} + 112 x^{34} + 448 x^{29} + 1120 x^{24} + 1792 x^{19} + 1792 x^{14} + 1024 x^{9} + 256 x^{4}

= 9 \cdot \int x^{44} + 16 x^{39} + 112 x^{34} + 448 x^{29} + 1120 x^{24} + 1792 x^{19} + 1792 x^{14} + 1024 x^{9} + 256 x^{4} 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

= 9 (\int x^{44} d x + \int 16 x^{39} d x + \int 112 x^{34} d x + \int 448 x^{29} d x + \int 1120 x^{24} d x + \int 1792 x^{19} d x + \int 1792 x^{14} d x + \int 1024 x^{9} d x + \int 256 x^{4} d x)

\int x^{44} d x = \frac{x ^{45}}{45}

\int 16 x^{39} d x = \frac{2 x ^{40}}{5}

\int 112 x^{34} d x = \frac{16 x ^{35}}{5}

\int 448 x^{29} d x = \frac{224 x ^{30}}{15}

\int 1120 x^{24} d x = \frac{224 x ^{25}}{5}

\int 1792 x^{19} d x = \frac{448 x ^{20}}{5}

\int 1792 x^{14} d x = \frac{1792 x ^{15}}{15}

\int 1024 x^{9} d x = \frac{512 x ^{10}}{5}

\int 256 x^{4} d x = \frac{256 x ^{5}}{5}

= 9 (\frac{x ^{45}}{45} + \frac{2 x ^{40}}{5} + \frac{16 x ^{35}}{5} + \frac{224 x ^{30}}{15} + \frac{224 x ^{25}}{5} + \frac{448 x ^{20}}{5} + \frac{1792 x ^{15}}{15} + \frac{512 x ^{10}}{5} + \frac{256 x ^{5}}{5})

Füge eine Konstante zur Lösung hinzu

= 9 (\frac{x ^{45}}{45} + \frac{2 x ^{40}}{5} + \frac{16 x ^{35}}{5} + \frac{224 x ^{30}}{15} + \frac{224 x ^{25}}{5} + \frac{448 x ^{20}}{5} + \frac{1792 x ^{15}}{15} + \frac{512 x ^{10}}{5} + \frac{256 x ^{5}}{5}) + C

Graph

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derivative-2e^{-x^2}

d er i v a t i v e - 2 e^{- x^{2}}

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d er i v a t i v e y = \frac{csc ( 4 x )}{ln ( x )}

x^2(d^2y)/(dx^2)+4x(dy)/(dx)+2y=8x

x^{2} \frac{d ^{2} y}{d x ^{2}} + 4 x \frac{d y}{d x} + 2 y = 8 x

tangent y=x^2-8

t an g e n t y = x^{2} - 8

integral of sqrt(x^2-a^2)

\int x^{2} - a^{2} d x