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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Vereinfache

x^{2} x : x^{\frac{5}{2}}

= \int \frac{x + 1}{x ^{\frac{5}{2}}} d x

Multipliziere aus

\frac{x + 1}{x ^{\frac{5}{2}}} : \frac{1}{x ^{\frac{3}{2}}} + \frac{1}{x ^{\frac{5}{2}}}

= \int \frac{1}{x ^{\frac{3}{2}}} + \frac{1}{x ^{\frac{5}{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 \frac{1}{x ^{\frac{3}{2}}} d x + \int \frac{1}{x ^{\frac{5}{2}}} d x

\int \frac{1}{x ^{\frac{3}{2}}} d x = - \frac{2}{x}

\int \frac{1}{x ^{\frac{5}{2}}} d x = - \frac{2}{3 x ^{\frac{3}{2}}}

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

Füge eine Konstante zur Lösung hinzu

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

Graph

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