integral of sqrt(x)(2+x)

Lösung

\int x (2 + x) d x

\frac{4}{3} x^{\frac{3}{2}} + \frac{2}{5} x^{\frac{5}{2}} + C

Schritte zur Lösung

\int x (2 + x) d x

Multipliziere aus

x (2 + x) : 2 x + x^{\frac{3}{2}}

= \int 2 x + x^{\frac{3}{2}} 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 x d x + \int x^{\frac{3}{2}} d x

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

\int x^{\frac{3}{2}} d x = \frac{2}{5} x^{\frac{5}{2}}

= \frac{4}{3} x^{\frac{3}{2}} + \frac{2}{5} x^{\frac{5}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{4}{3} x^{\frac{3}{2}} + \frac{2}{5} x^{\frac{5}{2}} + C

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