integral of x(3-x)

Lösung

\int x (3 - x) d x

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

Schritte zur Lösung

\int x (3 - x) d x

Multipliziere aus

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

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

\int \frac{5 e ^{x}}{e ^{2 x} + 6 e ^{x} + 9} d x

\int_{0}^{2} (4 x - x^{3}) d x

in v erse l a pl a ce \frac{( 4 s - 3 )}{( s ^{2} + 8 s + 24 )}

a re a x + 2 y = 7, x + 8 = y^{2}

\int 14 x^{6} y^{- 4} - 12 x^{5} y^{- 3} d x