integral of (6x^4+4)/(x^2)

Lösung

\int \frac{6 x ^{4} + 4}{x ^{2}} d x

2 x^{3} - \frac{4}{x} + C

Schritte zur Lösung

\int \frac{6 x ^{4} + 4}{x ^{2}} d x

Multipliziere aus

\frac{6 x ^{4} + 4}{x ^{2}} : 6 x^{2} + \frac{4}{x ^{2}}

= \int 6 x^{2} + \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 6 x^{2} d x + \int \frac{4}{x ^{2}} d x

\int 6 x^{2} d x = 2 x^{3}

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

= 2 x^{3} - \frac{4}{x}

Füge eine Konstante zur Lösung hinzu

= 2 x^{3} - \frac{4}{x} + C

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