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Beliebt Rechnen >

integral of (3-2x-4x^2)(1+4x)

Lösung

\int (3 - 2 x - 4 x^{2}) (1 + 4 x) d x

Lösung

3 x + 5 x^{2} - 4 x^{3} - 4 x^{4} + C

Schritte zur Lösung

\int (3 - 2 x - 4 x^{2}) (1 + 4 x) d x

Multipliziere aus

(3 - 2 x - 4 x^{2}) (1 + 4 x) : 3 + 10 x - 12 x^{2} - 16 x^{3}

= \int 3 + 10 x - 12 x^{2} - 16 x^{3} 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 3 d x + \int 10 x d x - \int 12 x^{2} d x - \int 16 x^{3} d x

\int 3 d x = 3 x

\int 10 x d x = 5 x^{2}

\int 12 x^{2} d x = 4 x^{3}

\int 16 x^{3} d x = 4 x^{4}

= 3 x + 5 x^{2} - 4 x^{3} - 4 x^{4}

Füge eine Konstante zur Lösung hinzu

= 3 x + 5 x^{2} - 4 x^{3} - 4 x^{4} + C

Graph

Beliebte Beispiele

integral of 10xsin(x)

\int 10 x sin (x) d x

tangent y=5+4x^2

t an g e n t y = 5 + 4 x^{2}

(\partial)/(\partial x)(12x^2y^3)

\frac{\partial}{\partial x} (12 x^{2} y^{3})

limit as x approaches 0+of (e^x+x)^{3/x}

x \to 0 + lim ((e^{x} + x)^{\frac{3}{x}})

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

\int \frac{1}{x ^{2} + 2 x + 3} d x