integral of (x^4+8sqrt(x))/(x^2)

Lösung

\int \frac{x ^{4} + 8 x}{x ^{2}} d x

\frac{x ^{3}}{3} - \frac{16}{x} + C

Schritte zur Lösung

\int \frac{x ^{4} + 8 x}{x ^{2}} d x

Multipliziere aus

\frac{x ^{4} + 8 x}{x ^{2}} : x^{2} + \frac{8}{x ^{\frac{3}{2}}}

= \int x^{2} + \frac{8}{x ^{\frac{3}{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^{2} d x + \int \frac{8}{x ^{\frac{3}{2}}} d x

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

\int \frac{8}{x ^{\frac{3}{2}}} d x = - \frac{16}{x}

= \frac{x ^{3}}{3} - \frac{16}{x}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{3}}{3} - \frac{16}{x} + C

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