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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{5 x ^{3}}{3} - 3 ln ∣ x ∣ + C

Schritte zur Lösung

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

Multipliziere aus

\frac{5 x ^{3} - 3}{x} : 5 x^{2} - \frac{3}{x}

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

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

\int \frac{3}{x} d x = 3 ln ∣ x ∣

= \frac{5 x ^{3}}{3} - 3 ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= \frac{5 x ^{3}}{3} - 3 ln ∣ x ∣ + C

Graph

Beliebte Beispiele

inverselaplace (8.75)/(S+2/3)

in v erse l a pl a ce \frac{8.75}{S + \frac{2}{3}}

derivative of (2x+5/(x^2+5x))

\frac{d}{d x} (\frac{2 x + 5}{x ^{2} + 5 x})

integral of (11)/((t^2+1)^{3/2)}

\int \frac{11}{( t ^{2} + 1 ) ^{\frac{3}{2}}} d t

derivative of (x^{(2})/(sin(x)))

\frac{d}{d x} (\frac{x ^{(2)}}{sin ( x )})

tangent f(x)=3^x,\at x=1

t an g e n t f (x) = 3^{x}, at x = 1