integral of (1-x)^2sqrt(x)

Lösung

\int (1 - x)^{2} x d x

\frac{2}{3} x^{\frac{3}{2}} - \frac{4}{5} x^{\frac{5}{2}} + \frac{2}{7} x^{\frac{7}{2}} + C

Schritte zur Lösung

\int (1 - x)^{2} x d x

Multipliziere aus

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

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

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

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

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

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

= \frac{2}{3} x^{\frac{3}{2}} - \frac{4}{5} x^{\frac{5}{2}} + \frac{2}{7} x^{\frac{7}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{2}{3} x^{\frac{3}{2}} - \frac{4}{5} x^{\frac{5}{2}} + \frac{2}{7} x^{\frac{7}{2}} + C

y^{^{''}} - 10 y^{^{'}} + 25 y = 0, y (0) = 7, y^{^{'}} (0) = 0

\int \frac{x + 3}{3 x ^{2} + 6 x} d x

d er i v a t i v e - 1.5 sin (1.5 x)

\int (9 x - 1) e^{- x} d x

\int (x + 6)^{2} d x