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Beliebt Rechnen >

integral of (3\sqrt[3]{x^4}-3x+2/x)

Lösung

\int (3 3 x^{4} - 3 x + \frac{2}{x}) d x

Lösung

\frac{9}{7} x^{\frac{7}{3}} - \frac{3 x ^{2}}{2} + 2 ln ∣ x ∣ + C

Schritte zur Lösung

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

\int 3 3 x^{4} d x = \frac{9}{7} x^{\frac{7}{3}}

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

\int \frac{2}{x} d x = 2 ln ∣ x ∣

= \frac{9}{7} x^{\frac{7}{3}} - \frac{3 x ^{2}}{2} + 2 ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= \frac{9}{7} x^{\frac{7}{3}} - \frac{3 x ^{2}}{2} + 2 ln ∣ x ∣ + C

Graph

Beliebte Beispiele

integral of xsqrt(3x^2-4)

\int x 3 x^{2} - 4 d x

integral of (5x)/((3-x^2)^3)

\int \frac{5 x}{( 3 - x ^{2} ) ^{3}} d x

integral of (1/x+3x^2+4)

\int (\frac{1}{x} + 3 x^{2} + 4) d x

integral of (e^{sqrt(r)})/(sqrt(r))

\int \frac{e ^{r}}{r} d r

integral of ((x^3+4x^2-x)/x)

\int (\frac{x ^{3} + 4 x ^{2} - x}{x}) d x