integral of x^{-4}+x^{1/3}

Lösung

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

- \frac{1}{3 x ^{3}} + \frac{3}{4} x^{\frac{4}{3}} + C

Schritte zur Lösung

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

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

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

= - \frac{1}{3 x ^{3}} + \frac{3}{4} x^{\frac{4}{3}}

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{3 x ^{3}} + \frac{3}{4} x^{\frac{4}{3}} + C

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