integral of (4-x)/(x^3)

Lösung

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

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

Schritte zur Lösung

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

Multipliziere aus

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

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

\int \frac{4}{x ^{3}} d x = - \frac{2}{x ^{2}}

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

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