integral of (27x^3-2)/(\sqrt[3]{x)}

Lösung

\int \frac{27 x ^{3} - 2}{3 x} d x

\frac{81}{11} x^{\frac{11}{3}} - 3 x^{\frac{2}{3}} + C

Schritte zur Lösung

\int \frac{27 x ^{3} - 2}{3 x} d x

Multipliziere aus

\frac{27 x ^{3} - 2}{3 x} : 27 x^{\frac{8}{3}} - \frac{2}{3 x}

= \int 27 x^{\frac{8}{3}} - \frac{2}{3 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 27 x^{\frac{8}{3}} d x - \int \frac{2}{3 x} d x

\int 27 x^{\frac{8}{3}} d x = \frac{81}{11} x^{\frac{11}{3}}

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

= \frac{81}{11} x^{\frac{11}{3}} - 3 x^{\frac{2}{3}}

Füge eine Konstante zur Lösung hinzu

= \frac{81}{11} x^{\frac{11}{3}} - 3 x^{\frac{2}{3}} + C

\int (x^{3} - e^{x^{4}}) d x

\int \frac{( 3 x ^{2} + 9 x + 1 )}{x} d x

\int \frac{sin ( 2 x )}{2 + 3 cos ( 2 x )} d x

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

\int sec^{7} (3 x) d x