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

Lösung

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

\frac{x ^{8}}{8} + \frac{2 x ^{5}}{5} + \frac{x ^{2}}{2} + C

Schritte zur Lösung

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

Multipliziere aus

(x^{3} + 1)^{2} x : x^{7} + 2 x^{4} + x

= \int x^{7} + 2 x^{4} + 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^{7} d x + \int 2 x^{4} d x + \int x d x

\int x^{7} d x = \frac{x ^{8}}{8}

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

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

= \frac{x ^{8}}{8} + \frac{2 x ^{5}}{5} + \frac{x ^{2}}{2}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{8}}{8} + \frac{2 x ^{5}}{5} + \frac{x ^{2}}{2} + C

x \to 3 lim (\frac{x + 3}{x + 2})

\frac{d}{d x} (\frac{7}{8 x ^{5}})

\frac{\partial}{\partial y} (y cos (z))

\frac{\partial}{\partial y} (z^{2})

\frac{\partial}{\partial x} (x y - x + y)