integral of (3-x)sqrt(x)

Lösung

\int (3 - x) x d x

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

Schritte zur Lösung

\int (3 - x) x d x

Multipliziere aus

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

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

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

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

= 2 x^{\frac{3}{2}} - \frac{2}{5} x^{\frac{5}{2}}

Füge eine Konstante zur Lösung hinzu

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

\int \frac{1}{4 x - x ^{2} - 3} d x

\int \frac{x ^{2}}{3 x ^{3} + 1} d x

\int (sin (ln (x))) d x

\int sec (x) sin (x) d x

\int ln (4 - 2 x) d x