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

Lösung

\int (\frac{2 x ^{3} - 3}{x}) d x

\frac{2 x ^{3}}{3} - 3 ln ∣ x ∣ + C

Schritte zur Lösung

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

Multipliziere aus

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

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

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

\int \frac{3}{x} d x = 3 ln ∣ x ∣

= \frac{2 x ^{3}}{3} - 3 ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= \frac{2 x ^{3}}{3} - 3 ln ∣ x ∣ + C

\int (\frac{sin ( 2 x )}{y} + x) d x

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

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

\int 8 cot^{4} (t) d t

\int \frac{1}{2 x ^{2} + 8 x + 10} d x