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Beliebt Rechnen >

integral of ((2x^2+x^2sqrt(x)-1))/(x^2)

Lösung

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

Lösung

2 x + \frac{2}{3} x^{\frac{3}{2}} + \frac{1}{x} + C

Schritte zur Lösung

\int \frac{2 x ^{2} + x ^{2} x - 1}{x ^{2}} d x

Multipliziere aus

\frac{2 x ^{2} + x ^{2} x - 1}{x ^{2}} : 2 + x - \frac{1}{x ^{2}}

= \int 2 + x - \frac{1}{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 d x + \int x d x - \int \frac{1}{x ^{2}} d x

\int 2 d x = 2 x

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

\int \frac{1}{x ^{2}} d x = - \frac{1}{x}

= 2 x + \frac{2}{3} x^{\frac{3}{2}} - (- \frac{1}{x})

Vereinfache

= 2 x + \frac{2}{3} x^{\frac{3}{2}} + \frac{1}{x}

Füge eine Konstante zur Lösung hinzu

= 2 x + \frac{2}{3} x^{\frac{3}{2}} + \frac{1}{x} + C

Graph

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