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Beliebt Rechnen >

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

Lösung

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

Lösung

x^{3} - \frac{x ^{2}}{2} - \frac{1}{4 x ^{2}} + C

Schritte zur Lösung

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

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

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

\int \frac{1}{2 x ^{3}} d x = - \frac{1}{4 x ^{2}}

= x^{3} - \frac{x ^{2}}{2} - \frac{1}{4 x ^{2}}

Füge eine Konstante zur Lösung hinzu

= x^{3} - \frac{x ^{2}}{2} - \frac{1}{4 x ^{2}} + C

Graph

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