integral of (-2x^{-3}+20x^{-5})

Lösung

\int (- 2 x^{- 3} + 20 x^{- 5}) d x

\frac{1}{x ^{2}} - \frac{5}{x ^{4}} + C

Schritte zur Lösung

\int - 2 x^{- 3} + 20 x^{- 5} d x

Vereinfache

- 2 x^{- 3} + 20 x^{- 5} : - \frac{2}{x ^{3}} + \frac{20}{x ^{5}}

= \int - \frac{2}{x ^{3}} + \frac{20}{x ^{5}} 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 ^{3}} d x + \int \frac{20}{x ^{5}} d x

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

\int \frac{20}{x ^{5}} d x = - \frac{5}{x ^{4}}

= - (- \frac{1}{x ^{2}}) - \frac{5}{x ^{4}}

Vereinfache

= \frac{1}{x ^{2}} - \frac{5}{x ^{4}}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{x ^{2}} - \frac{5}{x ^{4}} + C

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

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

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

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