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

Lösung

\int 2 + 4 - x + x d x

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

Schritte zur Lösung

\int 2 + 4 - x + 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 2 d x + \int 4 - x d x + \int x d x

\int 2 d x = 2 x

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

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

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

Füge eine Konstante zur Lösung hinzu

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

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