integral of (x^5+7)/(x^2)

Lösung

\int \frac{x ^{5} + 7}{x ^{2}} d x

\frac{x ^{4}}{4} - \frac{7}{x} + C

Schritte zur Lösung

\int \frac{x ^{5} + 7}{x ^{2}} d x

Multipliziere aus

\frac{x ^{5} + 7}{x ^{2}} : x^{3} + \frac{7}{x ^{2}}

= \int x^{3} + \frac{7}{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^{3} d x + \int \frac{7}{x ^{2}} d x

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

\int \frac{7}{x ^{2}} d x = - \frac{7}{x}

= \frac{x ^{4}}{4} - \frac{7}{x}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{4}}{4} - \frac{7}{x} + C

\frac{d}{d x} (\frac{1}{4 + x ^{2}})

\frac{d}{d x} (sin (x) + 3 cos (x))

\int x^{3} 5 - x^{2} d x

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