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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Multipliziere aus

\frac{( 1 + x ) ^{2}}{x} : \frac{1}{x} + 2 + x

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

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

\int 2 d x = 2 x

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of sqrt(1+4x-x^2)

\int 1 + 4 x - x^{2} d x

integral of arctan(1/x)

\int arctan (\frac{1}{x}) d x

derivative of 2x^2-4x+3

\frac{d}{d x} (2 x^{2} - 4 x + 3)

derivative f(x)=139+(36)/x+(x^2)/(16)

d er i v a t i v e f (x) = 139 + \frac{36}{x} + \frac{x ^{2}}{16}

x^{''}-6x^'+25x=64e^{-t}

x^{^{''}} - 6 x^{^{'}} + 25 x = 64 e^{- t}