integral of ((8+x+x^2))/(sqrt(x))

Lösung

\int \frac{( 8 + x + x ^{2} )}{x} d x

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

Schritte zur Lösung

\int \frac{8 + x + x ^{2}}{x} d x

Multipliziere aus

\frac{8 + x + x ^{2}}{x} : \frac{8}{x} + x + x^{\frac{3}{2}}

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

\int \frac{8}{x} d x = 16 x

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

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

= 16 x + \frac{2}{3} x^{\frac{3}{2}} + \frac{2}{5} x^{\frac{5}{2}}

Füge eine Konstante zur Lösung hinzu

= 16 x + \frac{2}{3} x^{\frac{3}{2}} + \frac{2}{5} x^{\frac{5}{2}} + C

x \to 4 - lim (\frac{6 x}{x - 4})

f (x) = 3 sin^{2} (x)

2 y^{^{''}} + y^{^{'}} - 2 y = 0

x \to 5 lim (cos (x))

d er i v a t i v e y = 2 x^{3 π}