integral of x^3-3x^2-x+3

Lösung

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

\frac{x ^{4}}{4} - x^{3} - \frac{x ^{2}}{2} + 3 x + C

Schritte zur Lösung

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

\int x^{3} d x = \frac{x ^{4}}{4}

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

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

\int 3 d x = 3 x

= \frac{x ^{4}}{4} - x^{3} - \frac{x ^{2}}{2} + 3 x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{4}}{4} - x^{3} - \frac{x ^{2}}{2} + 3 x + C

\frac{\partial}{\partial y} (3)

\int sin^{2} (6 x) d x

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

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

y^{^{'}} = (1 + x) (1 + y)