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

Lösung

\int x^{2} (x^{3} - 1)^{3} d x

\frac{x ^{12}}{12} - \frac{x ^{9}}{3} + \frac{x ^{6}}{2} - \frac{x ^{3}}{3} + C

Schritte zur Lösung

\int x^{2} (x^{3} - 1)^{3} d x

Multipliziere aus

x^{2} (x^{3} - 1)^{3} : x^{11} - 3 x^{8} + 3 x^{5} - x^{2}

= \int x^{11} - 3 x^{8} + 3 x^{5} - x^{2} 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^{11} d x - \int 3 x^{8} d x + \int 3 x^{5} d x - \int x^{2} d x

\int x^{11} d x = \frac{x ^{12}}{12}

\int 3 x^{8} d x = \frac{x ^{9}}{3}

\int 3 x^{5} d x = \frac{x ^{6}}{2}

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

= \frac{x ^{12}}{12} - \frac{x ^{9}}{3} + \frac{x ^{6}}{2} - \frac{x ^{3}}{3}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{12}}{12} - \frac{x ^{9}}{3} + \frac{x ^{6}}{2} - \frac{x ^{3}}{3} + C

a re a y = x, y = (x - 2)^{2}

x \to 0 lim (\frac{2 x}{x + 4})

\frac{d}{d x} (\frac{1 - tan ( x )}{1 + tan ( x )})

t an g e n t \frac{10 x}{x ^{2} - 6}

f (x) = x^{2} ln (x)