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

Lösung

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

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

Schritte zur Lösung

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

Multipliziere aus

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

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

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

\int 1 d x = x

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

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

Füge eine Konstante zur Lösung hinzu

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

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

\int \frac{1}{x \cdot x ^{2} - 2} d x

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