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Beliebt Rechnen >

integral of (6-x^3)/(xsqrt(x))

Lösung

\int \frac{6 - x ^{3}}{x x} d x

Lösung

- \frac{12}{x} - \frac{2}{5} x^{\frac{5}{2}} + C

Schritte zur Lösung

\int \frac{6 - x ^{3}}{x x} d x

Multipliziere aus

\frac{6 - x ^{3}}{x x} : \frac{6}{x x} - x^{\frac{3}{2}}

= \int \frac{6}{x x} - x^{\frac{3}{2}} 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{6}{x x} d x - \int x^{\frac{3}{2}} d x

\int \frac{6}{x x} d x = - \frac{12}{x}

\int x^{\frac{3}{2}} d x = \frac{2}{5} x^{\frac{5}{2}}

= - \frac{12}{x} - \frac{2}{5} x^{\frac{5}{2}}

Füge eine Konstante zur Lösung hinzu

= - \frac{12}{x} - \frac{2}{5} x^{\frac{5}{2}} + C

Graph

Beliebte Beispiele

integral of x^3-sec^2(x)

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

integral of 0/(x-1)

\int \frac{0}{x - 1} d x

integral of (xy)/(sqrt(1+x^2))

\int \frac{x y}{1 + x ^{2}} d x

integral of 11xsqrt(x^2+5)

\int 11 x x^{2} + 5 d x

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

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