integral of (2x+3)/(x^3)

Lösung

\int \frac{2 x + 3}{x ^{3}} d x

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

Schritte zur Lösung

\int \frac{2 x + 3}{x ^{3}} d x

Multipliziere aus

\frac{2 x + 3}{x ^{3}} : \frac{2}{x ^{2}} + \frac{3}{x ^{3}}

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

\int \frac{4 x ^{2}}{( x - 8 ) ^{2} ( x + 8 )} d x

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