integral of ((x^2-1))/(x^{3/2)}

Lösung

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

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

Schritte zur Lösung

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

Multipliziere aus

\frac{x ^{2} - 1}{x ^{\frac{3}{2}}} : x^{\frac{1}{2}} - \frac{1}{x ^{\frac{3}{2}}}

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

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

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

\frac{d}{d x} (a - x)

\int x 6^{x} d x

x \to 9 + lim (\frac{5 x}{x - 9})

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\frac{d ^{4}}{d x ^{4}} (\frac{1}{1 + x})