integral of (x^3+x)/(x^2)

Lösung

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

\frac{x ^{2}}{2} + ln ∣ x ∣ + C

Schritte zur Lösung

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

Multipliziere aus

\frac{x ^{3} + x}{x ^{2}} : x + \frac{1}{x}

= \int x + \frac{1}{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 x d x + \int \frac{1}{x} d x

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

\int \frac{1}{x} d x = ln ∣ x ∣

= \frac{x ^{2}}{2} + ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{2}}{2} + ln ∣ x ∣ + C

\frac{\partial}{\partial x} (2 x^{3} y + cos (x^{2}))

\frac{d}{d x} (\frac{x + 2}{x - 2})

\int (\frac{9 + x + x}{x}) d x

\int (2 x + 5) e^{x} d x

y^{^{'}} - 2 x y = e^{x^{2}}