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

Lösung

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

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

Schritte zur Lösung

\int x^{3} - 3 x^{2} + 2 x + 1 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 2 x d x + \int 1 d x

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

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

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

\int 1 d x = x

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

Füge eine Konstante zur Lösung hinzu

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

\int \frac{2 x ^{3} + 5 x ^{2} - 2 x}{x} d x

d er i v a t i v e r (t) - 4 tan (5 t^{3})

x \to 2 lim (\frac{( 1 )}{( x + 2 )})

d er i v a t i v e y = x^{2} sin (4 x)

y^{^{''}} + 4 y^{^{'}} + 4 y = 0, y (0) = 0, y^{^{'}} (0) = 1