integral of 5x^4+2x^{-3}-3e^x+2/3 x^{-1}

Lösung

\int 5 x^{4} + 2 x^{- 3} - 3 e^{x} + \frac{2}{3} x^{- 1} d x

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

Schritte zur Lösung

\int 5 x^{4} + 2 x^{- 3} - 3 e^{x} + \frac{2}{3} x^{- 1} 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 5 x^{4} d x + \int 2 x^{- 3} d x - \int 3 e^{x} d x + \int \frac{2}{3} x^{- 1} d x

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

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

\int 3 e^{x} d x = 3 e^{x}

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

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

Füge eine Konstante zur Lösung hinzu

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