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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{x ^{2}}{2} + \frac{3}{4 x ^{4}} + C

Schritte zur Lösung

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

Multipliziere aus

\frac{x ^{7} - 3 x}{x ^{6}} : x - \frac{3}{x ^{5}}

= \int x - \frac{3}{x ^{5}} 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 x d x - \int \frac{3}{x ^{5}} d x

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

\int \frac{3}{x ^{5}} d x = - \frac{3}{4 x ^{4}}

= \frac{x ^{2}}{2} - (- \frac{3}{4 x ^{4}})

Vereinfache

= \frac{x ^{2}}{2} + \frac{3}{4 x ^{4}}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{2}}{2} + \frac{3}{4 x ^{4}} + C

Graph

Beliebte Beispiele

integral of (4x)/(2x)+6

\int \frac{4 x}{2 x} + 6 d x

integral of x(x^2-7)^{7/2}

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

integral of (x-1)(x+3)

\int (x - 1) (x + 3) d x

integral of (arctan^3(3x))/(1+9x^2)

\int \frac{arctan ^{3} ( 3 x )}{1 + 9 x ^{2}} d x

integral of x^ncos(a)x

\int x^{n} cos (a) x d x