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Beliebt Rechnen >

integral of (sqrt(x)-x+5)/(x^4)

Lösung

\int \frac{x - x + 5}{x ^{4}} d x

Lösung

- \frac{2}{5 x ^{\frac{5}{2}}} + \frac{1}{2 x ^{2}} - \frac{5}{3 x ^{3}} + C

Schritte zur Lösung

\int \frac{x - x + 5}{x ^{4}} d x

Multipliziere aus

\frac{x - x + 5}{x ^{4}} : \frac{1}{x ^{\frac{7}{2}}} - \frac{1}{x ^{3}} + \frac{5}{x ^{4}}

= \int \frac{1}{x ^{\frac{7}{2}}} - \frac{1}{x ^{3}} + \frac{5}{x ^{4}} 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{7}{2}}} d x - \int \frac{1}{x ^{3}} d x + \int \frac{5}{x ^{4}} d x

\int \frac{1}{x ^{\frac{7}{2}}} d x = - \frac{2}{5 x ^{\frac{5}{2}}}

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

\int \frac{5}{x ^{4}} d x = - \frac{5}{3 x ^{3}}

= - \frac{2}{5 x ^{\frac{5}{2}}} - (- \frac{1}{2 x ^{2}}) - \frac{5}{3 x ^{3}}

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

= - \frac{2}{5 x ^{\frac{5}{2}}} + \frac{1}{2 x ^{2}} - \frac{5}{3 x ^{3}} + C

Graph

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