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Beliebt Rechnen >

integral of ((7-4x^3+6x^6))/(x^6)

Lösung

\int \frac{( 7 - 4 x ^{3} + 6 x ^{6} )}{x ^{6}} d x

Lösung

- \frac{7}{5 x ^{5}} + \frac{2}{x ^{2}} + 6 x + C

Schritte zur Lösung

\int \frac{7 - 4 x ^{3} + 6 x ^{6}}{x ^{6}} d x

Multipliziere aus

\frac{7 - 4 x ^{3} + 6 x ^{6}}{x ^{6}} : \frac{7}{x ^{6}} - \frac{4}{x ^{3}} + 6

= \int \frac{7}{x ^{6}} - \frac{4}{x ^{3}} + 6 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

= \int \frac{7}{x ^{6}} d x - \int \frac{4}{x ^{3}} d x + \int 6 d x

\int \frac{7}{x ^{6}} d x = - \frac{7}{5 x ^{5}}

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

\int 6 d x = 6 x

= - \frac{7}{5 x ^{5}} - (- \frac{2}{x ^{2}}) + 6 x

Vereinfache

= - \frac{7}{5 x ^{5}} + \frac{2}{x ^{2}} + 6 x

Füge eine Konstante zur Lösung hinzu

= - \frac{7}{5 x ^{5}} + \frac{2}{x ^{2}} + 6 x + C

Graph

Beliebte Beispiele

derivative of x^5(2x-1^7)

\frac{d}{d x} (x^{5} (2 x - 1)^{7})

derivative of (x+7/(x^3+x-6))

\frac{d}{d x} (\frac{x + 7}{x ^{3} + x - 6})

limit as x approaches 1 of |-x^2+1|

x \to 1 lim (- x^{2} + 1)

x*(dy)/(dx)+7y= 1/x

x \cdot \frac{d y}{d x} + 7 y = \frac{1}{x}

integral of e^{5x}sin(5x)

\int e^{5 x} sin (5 x) d x