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Beliebt Rechnen >

integral of (-10x^4-2x^{-3}+15x^{-4})

Lösung

\int (- 10 x^{4} - 2 x^{- 3} + 15 x^{- 4}) d x

Lösung

- 2 x^{5} + \frac{1}{x ^{2}} - \frac{5}{x ^{3}} + C

Schritte zur Lösung

\int - 10 x^{4} - 2 x^{- 3} + 15 x^{- 4} 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 10 x^{4} d x - \int 2 x^{- 3} d x + \int 15 x^{- 4} d x

\int 10 x^{4} d x = 2 x^{5}

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

\int 15 x^{- 4} d x = - \frac{5}{x ^{3}}

= - 2 x^{5} - (- \frac{1}{x ^{2}}) - \frac{5}{x ^{3}}

Vereinfache

= - 2 x^{5} + \frac{1}{x ^{2}} - \frac{5}{x ^{3}}

Füge eine Konstante zur Lösung hinzu

= - 2 x^{5} + \frac{1}{x ^{2}} - \frac{5}{x ^{3}} + C

Graph

Beliebte Beispiele

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

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\int \frac{cos ^{5} ( x )}{sin ^{4} ( x )} d x

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\int \frac{1}{x 4 x + 25} d x

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

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