integral of (2/(x^4)-3/(x^3)+1/(x^2))

Lösung

\int (\frac{2}{x ^{4}} - \frac{3}{x ^{3}} + \frac{1}{x ^{2}}) d x

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

Schritte zur Lösung

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

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

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

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

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