integral of (x^3+x^2-x+1)/x

Lösung

\int \frac{x ^{3} + x ^{2} - x + 1}{x} d x

\frac{x ^{3}}{3} + \frac{x ^{2}}{2} - x + ln ∣ x ∣ + C

Schritte zur Lösung

\int \frac{x ^{3} + x ^{2} - x + 1}{x} d x

Multipliziere aus

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

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

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

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

\int 1 d x = x

\int \frac{1}{x} d x = ln ∣ x ∣

= \frac{x ^{3}}{3} + \frac{x ^{2}}{2} - x + ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{3}}{3} + \frac{x ^{2}}{2} - x + ln ∣ x ∣ + C

\frac{d}{d x} (e^{x^{3} l n (x)})

\frac{\partial}{\partial x} (3 x^{2} y^{4} + 3)

f (x) = \frac{cos ( 2 x ) ln ( x )}{x - 5}

\int x \cdot e^{6 x} d x

a re a 2 (x - 1)^{2} + 50, 3 (x + 3)^{2} + 2