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Beliebt Rechnen >

integral of (3sqrt(x)+7)/(\sqrt[3]{x)}

Lösung

\int \frac{3 x + 7}{3 x} d x

Lösung

\frac{18}{7} x^{\frac{7}{6}} + \frac{21}{2} x^{\frac{2}{3}} + C

Schritte zur Lösung

\int \frac{3 x + 7}{3 x} d x

Multipliziere aus

\frac{3 x + 7}{3 x} : 3 6 x + \frac{7}{3 x}

= \int 3 6 x + \frac{7}{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 3 6 x d x + \int \frac{7}{3 x} d x

\int 3 6 x d x = \frac{18}{7} x^{\frac{7}{6}}

\int \frac{7}{3 x} d x = \frac{21}{2} x^{\frac{2}{3}}

= \frac{18}{7} x^{\frac{7}{6}} + \frac{21}{2} x^{\frac{2}{3}}

Füge eine Konstante zur Lösung hinzu

= \frac{18}{7} x^{\frac{7}{6}} + \frac{21}{2} x^{\frac{2}{3}} + C

Graph

Beliebte Beispiele

integral of x^3(3-x^4)^{10}

\int x^{3} (3 - x^{4})^{10} d x

integral of x(6x+7)^8

\int x (6 x + 7)^{8} d x

integral of x*x^{10}

\int x \cdot x^{10} d x

(dy)/(dx)y=x^{8cos(x)}

\frac{d y}{d x} y = x^{8 c o s (x)}

limit as x approaches 0 of (sin(5x))/(sin(1/3 x))

x \to 0 lim (\frac{sin ( 5 x )}{sin ( \frac{1}{3} x )})