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

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

\frac{d y}{d x} = \frac{x ^{2} - y ^{2}}{x y}, y (2) = 2

a re a 4 x, x^{2} - 5

\int se x (x)

a re a f (x) = x^{2} - 4, 1, 3