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Beliebt Rechnen >

integral of (4x^{19}-5x^{-8})/(x^2)

Lösung

\int \frac{4 x ^{19} - 5 x ^{- 8}}{x ^{2}} d x

Lösung

\frac{2 x ^{18}}{9} + \frac{5}{9 x ^{9}} + C

Schritte zur Lösung

\int \frac{4 x ^{19} - 5 x ^{- 8}}{x ^{2}} d x

Multipliziere aus

\frac{4 x ^{19} - 5 x ^{- 8}}{x ^{2}} : 4 x^{17} - \frac{5}{x ^{10}}

= \int 4 x^{17} - \frac{5}{x ^{10}} 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 4 x^{17} d x - \int \frac{5}{x ^{10}} d x

\int 4 x^{17} d x = \frac{2 x ^{18}}{9}

\int \frac{5}{x ^{10}} d x = - \frac{5}{9 x ^{9}}

= \frac{2 x ^{18}}{9} - (- \frac{5}{9 x ^{9}})

Vereinfache

= \frac{2 x ^{18}}{9} + \frac{5}{9 x ^{9}}

Füge eine Konstante zur Lösung hinzu

= \frac{2 x ^{18}}{9} + \frac{5}{9 x ^{9}} + C

Graph

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