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Beliebt Rechnen >

integral of (2-1/(x^5)+7/(x^3))

Lösung

\int (2 - \frac{1}{x ^{5}} + \frac{7}{x ^{3}}) d x

Lösung

2 x + \frac{1}{4 x ^{4}} - \frac{7}{2 x ^{2}} + C

Schritte zur Lösung

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

\int 2 d x = 2 x

\int \frac{1}{x ^{5}} d x = - \frac{1}{4 x ^{4}}

\int \frac{7}{x ^{3}} d x = - \frac{7}{2 x ^{2}}

= 2 x - (- \frac{1}{4 x ^{4}}) - \frac{7}{2 x ^{2}}

Vereinfache

= 2 x + \frac{1}{4 x ^{4}} - \frac{7}{2 x ^{2}}

Füge eine Konstante zur Lösung hinzu

= 2 x + \frac{1}{4 x ^{4}} - \frac{7}{2 x ^{2}} + C

Graph

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