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Beliebt Rechnen >

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

Lösung

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

Lösung

ln ∣ x ∣ + 2 x + \frac{x ^{2}}{2} + C

Schritte zur Lösung

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

Vereinfache

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

= \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 = ln ∣ x ∣

\int 2 d x = 2 x

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

= ln ∣ x ∣ + 2 x + \frac{x ^{2}}{2}

Füge eine Konstante zur Lösung hinzu

= ln ∣ x ∣ + 2 x + \frac{x ^{2}}{2} + C

Graph

Beliebte Beispiele

(\partial)/(\partial x)(sin(x+e^y))

\frac{\partial}{\partial x} (sin (x + e^{y}))

8x-6ysqrt(x^2+1)(dy)/(dx)=0

8 x - 6 y x^{2} + 1 \frac{d y}{d x} = 0

integral of (5-3x)^7

\int (5 - 3 x)^{7} d x

integral of 2x^{-5}

\int 2 x^{- 5} d x

(\partial)/(\partial y)(5y-e^{8sin(x)})

\frac{\partial}{\partial y} (5 y - e^{8 s i n (x)})