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Beliebt Rechnen >

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

Lösung

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

Lösung

in (\frac{x ^{2}}{2} + \frac{1}{2} x 1 + x^{2} + \frac{1}{2} ln x + 1 + x^{2}) + C

Schritte zur Lösung

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

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= in \cdot \int x + x^{2} + 1 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

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

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

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

= in (\frac{x ^{2}}{2} + \frac{1}{2} x 1 + x^{2} + \frac{1}{2} ln x + 1 + x^{2})

Füge eine Konstante zur Lösung hinzu

= in (\frac{x ^{2}}{2} + \frac{1}{2} x 1 + x^{2} + \frac{1}{2} ln x + 1 + x^{2}) + C

Graph

Beliebte Beispiele

(\partial)/(\partial y)(xe^{y-1})

\frac{\partial}{\partial y} (x e^{y - 1})

(dx)/(dt)=1.5-(2x)/(100+t)

\frac{d x}{d t} = 1.5 - \frac{2 x}{100 + t}

integral of x(x-6)^2

\int x (x - 6)^{2} d x

integral of 2e^{-x/5}

\int 2 e^{- \frac{x}{5}} d x

(\partial)/(\partial y)(y/((x+2)^2))

\frac{\partial}{\partial y} (\frac{y}{( x + 2 ) ^{2}})