integral of (x^2+5x+12)/(sqrt(x))

Lösung

\int \frac{x ^{2} + 5 x + 12}{x} d x

\frac{2}{5} x^{\frac{5}{2}} + \frac{10}{3} x^{\frac{3}{2}} + 24 x + C

Schritte zur Lösung

\int \frac{x ^{2} + 5 x + 12}{x} d x

Multipliziere aus

\frac{x ^{2} + 5 x + 12}{x} : x^{\frac{3}{2}} + 5 x + \frac{12}{x}

= \int x^{\frac{3}{2}} + 5 x + \frac{12}{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 5 x d x + \int \frac{12}{x} d x

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

\int 5 x d x = \frac{10}{3} x^{\frac{3}{2}}

\int \frac{12}{x} d x = 24 x

= \frac{2}{5} x^{\frac{5}{2}} + \frac{10}{3} x^{\frac{3}{2}} + 24 x

Füge eine Konstante zur Lösung hinzu

= \frac{2}{5} x^{\frac{5}{2}} + \frac{10}{3} x^{\frac{3}{2}} + 24 x + C