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Beliebt Rechnen >

integral of (sqrt(x)+sqrt(a))^2

Lösung

\int (x + a)^{2} d x

Lösung

\frac{x ^{2}}{2} + \frac{4}{3} a x^{\frac{3}{2}} + a x + C

Schritte zur Lösung

\int (x + a)^{2} d x

Multipliziere aus

(x + a)^{2} : x + 2 a x + a

= \int x + 2 a x + a 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 x d x + \int 2 a x d x + \int a d x

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

\int 2 a x d x = \frac{4}{3} a x^{\frac{3}{2}}

\int a d x = a x

= \frac{x ^{2}}{2} + \frac{4}{3} a x^{\frac{3}{2}} + a x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{2}}{2} + \frac{4}{3} a x^{\frac{3}{2}} + a x + C

Graph

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