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Beliebt Rechnen >

integral of x(2x-1)^2

Lösung

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

Lösung

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

Schritte zur Lösung

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

Multipliziere aus

x (2 x - 1)^{2} : 4 x^{3} - 4 x^{2} + x

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

\int 4 x^{3} d x = x^{4}

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

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of (2x+1)/(2x-1)

\int \frac{2 x + 1}{2 x - 1} d x

integral of x/(x^2-x)

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

integral of (x-2)/(sqrt(x+1))

\int \frac{x - 2}{x + 1} d x

integral of e^{3x}(3^x-e^{-2x})

\int e^{3 x} (3^{x} - e^{- 2 x}) d x

integral of ((x+1)e^x)/((x+2)^2)

\int \frac{( x + 1 ) e ^{x}}{( x + 2 ) ^{2}} d x