integral of (2x^3+5x^2-2x)/x

Lösung

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

\frac{2 x ^{3}}{3} + \frac{5 x ^{2}}{2} - 2 x + C

Schritte zur Lösung

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

Vereinfache

\frac{2 x ^{3} + 5 x ^{2} - 2 x}{x} : 2 x^{2} + 5 x - 2

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

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

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

\int 2 d x = 2 x

= \frac{2 x ^{3}}{3} + \frac{5 x ^{2}}{2} - 2 x

Füge eine Konstante zur Lösung hinzu

= \frac{2 x ^{3}}{3} + \frac{5 x ^{2}}{2} - 2 x + C

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

9 x^{2} y^{^{'}} = y^{^{'}} + 5 x e^{- y}