integral of ((x^{-1/3}-5))/x

Lösung

\int \frac{( x ^{- \frac{1}{3}} - 5 )}{x} d x

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

Schritte zur Lösung

\int \frac{x ^{- \frac{1}{3}} - 5}{x} d x

Multipliziere aus

\frac{x ^{- \frac{1}{3}} - 5}{x} : \frac{1}{x ^{\frac{4}{3}}} - \frac{5}{x}

= \int \frac{1}{x ^{\frac{4}{3}}} - \frac{5}{x} 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{1}{x ^{\frac{4}{3}}} d x - \int \frac{5}{x} d x

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

\int \frac{5}{x} d x = 5 ln ∣ x ∣

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

Füge eine Konstante zur Lösung hinzu

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

\int cot^{5} (\frac{x}{3}) d x

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

\int y cos (x y) + 1 d x

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

\int (1 - x^{2}) cos (nπ x) d x