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