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

Lösung

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

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

Schritte zur Lösung

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

Multipliziere aus

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

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

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

\int 2 d x = 2 x

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

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

Füge eine Konstante zur Lösung hinzu

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

\int \frac{1}{4 - u ^{2}} d u

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