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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

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

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

\int 1 d x = x

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

Graph

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