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

Lösung

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

\frac{4 x ^{3}}{3} + 3 x + 3 ln ∣ x ∣ + C

Schritte zur Lösung

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

Multipliziere aus

\frac{4 x ^{3} + 3 x + 3}{x} : 4 x^{2} + 3 + \frac{3}{x}

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

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

\int 3 d x = 3 x

\int \frac{3}{x} d x = 3 ln ∣ x ∣

= \frac{4 x ^{3}}{3} + 3 x + 3 ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= \frac{4 x ^{3}}{3} + 3 x + 3 ln ∣ x ∣ + C

x \to 7 lim (sin (\frac{π}{x}))

\frac{\partial}{\partial y} (\frac{y}{x - 1})

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

\frac{d}{d x} (\frac{1}{3 x - 4})

\frac{d}{d x} (2.2716 e^{0.2865 x})