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Beliebt Rechnen >

integral of x/(x+1-sqrt(x+1))

Lösung

\int \frac{x}{x + 1 - x + 1} d x

Lösung

x + 1 + 2 x + 1 + C

Schritte zur Lösung

\int \frac{x}{x + 1 - x + 1} d x

Wende U-Substitution an

= \int 2 (u + 1) d u

Entferne die Konstante:

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

= 2 \cdot \int u + 1 d u

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 2 (\int u d u + \int 1 d u)

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

\int 1 d u = u

= 2 (\frac{u ^{2}}{2} + u)

Setze in

u = x + 1

ein

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

Vereinfache

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

= x + 1 + 2 x + 1

Füge eine Konstante zur Lösung hinzu

= x + 1 + 2 x + 1 + C

Graph

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