integral of (x+1)/(sqrt(x^5))

Lösung

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

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

Schritte zur Lösung

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

Multipliziere aus

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

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

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

\int \frac{1}{x ^{5}} 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

x^{2} y^{^{''}} + 2 x y^{^{'}} - 20 y = 0

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