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

Lösung

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

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

Schritte zur Lösung

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

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

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

\int 2 d x = 2 x

= \frac{x ^{4}}{4} - (- \frac{2}{x}) + 2 x

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

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