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Beliebt Rechnen >

integral of x(x-1)^5

Lösung

\int x (x - 1)^{5} d x

Lösung

\frac{( x - 1 ) ^{7}}{7} + \frac{( x - 1 ) ^{6}}{6} + C

Schritte zur Lösung

\int x (x - 1)^{5} d x

Wende U-Substitution an

= \int (u + 1) u^{5} d u

Multipliziere aus

(u + 1) u^{5} : u^{6} + u^{5}

= \int u^{6} + u^{5} d u

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int u^{6} d u + \int u^{5} d u

\int u^{6} d u = \frac{u ^{7}}{7}

\int u^{5} d u = \frac{u ^{6}}{6}

= \frac{u ^{7}}{7} + \frac{u ^{6}}{6}

Setze in

u = x - 1

ein

= \frac{( x - 1 ) ^{7}}{7} + \frac{( x - 1 ) ^{6}}{6}

Füge eine Konstante zur Lösung hinzu

= \frac{( x - 1 ) ^{7}}{7} + \frac{( x - 1 ) ^{6}}{6} + C

Graph

Beliebte Beispiele

(\partial)/(\partial x)(y^{1/3}x^{2/3})

\frac{\partial}{\partial x} (y^{\frac{1}{3}} x^{\frac{2}{3}})

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

\int \frac{1}{( x - 1 ) ( x + 1 )} d x

derivative f(x)=x^3-2x^2-4x-6

d er i v a t i v e f (x) = x^{3} - 2 x^{2} - 4 x - 6

integral of (2x+5)e^{2x+5}

\int (2 x + 5) e^{2 x + 5} d x

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d er i v a t i v e - \frac{9}{2} x^{2} + 3 x + 3