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

Lösung

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

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

Schritte zur Lösung

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

Multipliziere aus

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

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

\int \frac{5}{x} d x = 10 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}}

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

Füge eine Konstante zur Lösung hinzu

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

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x \to - 2 lim (- x^{2} - 4 x)

x \to 0 - lim (x^{2} + \frac{1}{x})

ma c l a u r in \frac{2}{1 - x ^{2}}

\int \frac{1}{4 e ^{- 6 x} + e ^{6 x}} d x