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Beliebt Rechnen >

integral of ((6x-3)/(sqrt(x)))

Lösung

\int (\frac{6 x - 3}{x}) d x

Lösung

4 x^{\frac{3}{2}} - 6 x + C

Schritte zur Lösung

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

Multipliziere aus

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

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

\int 6 x d x = 4 x^{\frac{3}{2}}

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

= 4 x^{\frac{3}{2}} - 6 x

Füge eine Konstante zur Lösung hinzu

= 4 x^{\frac{3}{2}} - 6 x + C

Graph

Beliebte Beispiele

integral of 4x^2cos(x)

\int 4 x^{2} cos (x) d x

integral of 6x^2-4x+2

\int 6 x^{2} - 4 x + 2 d x

integral of (x^2+x)/(x^2-1)

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

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

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

integral of 1/(x^{3/4)-x^{1/4}}

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