integral of (x^2+4x-4)/(sqrt(x))

Lösung

\int \frac{x ^{2} + 4 x - 4}{x} d x

\frac{2}{5} x^{\frac{5}{2}} + \frac{8}{3} x^{\frac{3}{2}} - 8 x + C

Schritte zur Lösung

\int \frac{x ^{2} + 4 x - 4}{x} d x

Multipliziere aus

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

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

\int x^{\frac{3}{2}} d x = \frac{2}{5} x^{\frac{5}{2}}

\int 4 x d x = \frac{8}{3} x^{\frac{3}{2}}

\int \frac{4}{x} d x = 8 x

= \frac{2}{5} x^{\frac{5}{2}} + \frac{8}{3} x^{\frac{3}{2}} - 8 x

Füge eine Konstante zur Lösung hinzu

= \frac{2}{5} x^{\frac{5}{2}} + \frac{8}{3} x^{\frac{3}{2}} - 8 x + C

d er i v a t i v e f (x) = 6 x^{3} - 7 x

in v erse l a pl a ce \frac{( e ^{- 3 s} )}{s ^{2}}

\frac{\partial}{\partial y} (3 x + x^{2} y)

\frac{d y}{d x} = \frac{( 2 x ( y - 2 ) )}{x ^{2} + 1}, y (0) = 4

t \to 0 lim (e^{- t})