integral of ((x^2+1)/(sqrt(x)))

Lösung

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

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

Schritte zur Lösung

\int \frac{x ^{2} + 1}{x} d x

Multipliziere aus

\frac{x ^{2} + 1}{x} : x^{\frac{3}{2}} + \frac{1}{x}

= \int x^{\frac{3}{2}} + \frac{1}{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 \frac{1}{x} d x

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

\int \frac{1}{x} d x = 2 x

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

Füge eine Konstante zur Lösung hinzu

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

x^{2} y^{^{''}} - 7 x y^{^{'}} + 16 y = 0

a re a y = - 3 x^{3} + x^{2} + 10 x, x \geq 0

y^{^{''}} - 2 y^{^{'}} - 3 y = x e^{x}

d er i v a t i v e e^{\frac{4}{5} x}

\frac{d}{d x} (x + 1 - 2)