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Beliebt Rechnen >

integral of (3x^2+7sqrt(x)+1/(x^3))

Lösung

\int (3 x^{2} + 7 x + \frac{1}{x ^{3}}) d x

Lösung

x^{3} + \frac{14}{3} x^{\frac{3}{2}} - \frac{1}{2 x ^{2}} + C

Schritte zur Lösung

\int 3 x^{2} + 7 x + \frac{1}{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 x^{2} d x + \int 7 x d x + \int \frac{1}{x ^{3}} d x

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

\int 7 x d x = \frac{14}{3} x^{\frac{3}{2}}

\int \frac{1}{x ^{3}} d x = - \frac{1}{2 x ^{2}}

= x^{3} + \frac{14}{3} x^{\frac{3}{2}} - \frac{1}{2 x ^{2}}

Füge eine Konstante zur Lösung hinzu

= x^{3} + \frac{14}{3} x^{\frac{3}{2}} - \frac{1}{2 x ^{2}} + C

Graph

Beliebte Beispiele

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\int 2 x^{14} d x

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\int \frac{u - 1}{u} d u

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\int e^{2 x} + e^{2 x} d x

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\int \frac{cos ( x )}{3 - sin ^{2} ( x )} d x