integral of sqrt(2x)og(2-x)x

Lösung

\int 2 x o g (2 - x) x

o g (\frac{4 2}{5} x^{\frac{5}{2}} - 2 \frac{2}{7} x^{\frac{7}{2}}) + C

Schritte zur Lösung

\int 2 x o g (2 - x) x d x

Entferne die Konstante:

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

= o g \cdot \int (2 - x) 2 x x d x

Multipliziere aus

(2 - x) 2 x x : 2^{\frac{3}{2}} x^{\frac{3}{2}} - 2 x^{\frac{5}{2}}

= o g \cdot \int 2^{\frac{3}{2}} x^{\frac{3}{2}} - 2 x^{\frac{5}{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

= o g (\int 2^{\frac{3}{2}} x^{\frac{3}{2}} d x - \int 2 x^{\frac{5}{2}} d x)

\int 2^{\frac{3}{2}} x^{\frac{3}{2}} d x = \frac{4 2}{5} x^{\frac{5}{2}}

\int 2 x^{\frac{5}{2}} d x = 2 \frac{2}{7} x^{\frac{7}{2}}

= o g (\frac{4 2}{5} x^{\frac{5}{2}} - 2 \frac{2}{7} x^{\frac{7}{2}})

Füge eine Konstante zur Lösung hinzu

= o g (\frac{4 2}{5} x^{\frac{5}{2}} - 2 \frac{2}{7} x^{\frac{7}{2}}) + C

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