integral of 2sqrt(x)-x-9/(x^2)

Lösung

\int 2 x - x - \frac{9}{x ^{2}} d x

\frac{4}{3} x^{\frac{3}{2}} - \frac{x ^{2}}{2} + \frac{9}{x} + C

Schritte zur Lösung

\int 2 x - x - \frac{9}{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 2 x d x - \int x d x - \int \frac{9}{x ^{2}} d x

\int 2 x d x = \frac{4}{3} x^{\frac{3}{2}}

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

\int \frac{9}{x ^{2}} d x = - \frac{9}{x}

= \frac{4}{3} x^{\frac{3}{2}} - \frac{x ^{2}}{2} - (- \frac{9}{x})

Vereinfache

= \frac{4}{3} x^{\frac{3}{2}} - \frac{x ^{2}}{2} + \frac{9}{x}

Füge eine Konstante zur Lösung hinzu

= \frac{4}{3} x^{\frac{3}{2}} - \frac{x ^{2}}{2} + \frac{9}{x} + C

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