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Beliebt Rechnen >

integral of ((x-2)(x+3))/(xsqrt(x))

Lösung

\int \frac{( x - 2 ) ( x + 3 )}{x x} d x

Lösung

\frac{2}{3} x^{\frac{3}{2}} + 2 x + \frac{12}{x} + C

Schritte zur Lösung

\int \frac{( x - 2 ) ( x + 3 )}{x x} d x

Multipliziere aus

\frac{( x - 2 ) ( x + 3 )}{x x} : x + \frac{1}{x} - \frac{6}{x x}

= \int x + \frac{1}{x} - \frac{6}{x x} 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 d x + \int \frac{1}{x} d x - \int \frac{6}{x x} d x

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

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

\int \frac{6}{x x} d x = - \frac{12}{x}

= \frac{2}{3} x^{\frac{3}{2}} + 2 x - (- \frac{12}{x})

Vereinfache

= \frac{2}{3} x^{\frac{3}{2}} + 2 x + \frac{12}{x}

Füge eine Konstante zur Lösung hinzu

= \frac{2}{3} x^{\frac{3}{2}} + 2 x + \frac{12}{x} + C

Graph

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