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

Lösung

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

\frac{x ^{6}}{6} - \frac{2 x ^{5}}{5} + C

Schritte zur Lösung

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

Multipliziere aus

x^{3} (x^{2} - 2 x) : x^{5} - 2 x^{4}

= \int x^{5} - 2 x^{4} 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^{5} d x - \int 2 x^{4} d x

\int x^{5} d x = \frac{x ^{6}}{6}

\int 2 x^{4} d x = \frac{2 x ^{5}}{5}

= \frac{x ^{6}}{6} - \frac{2 x ^{5}}{5}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{6}}{6} - \frac{2 x ^{5}}{5} + C

\frac{d}{d x} ((5 x^{2} - 4 x) e^{x})

d er i v a t i v e 3 x e^{\frac{- 1}{y ^{3}}}

\int cos^{6} (x) sin (x) d x

d er i v a t i v e y = 11 + cot^{2} (x)

\frac{d}{d x} (I n (x))