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

Lösung

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

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

Schritte zur Lösung

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

Multipliziere aus

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

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

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