integral of+(1+sqrt(x))^3

Lösung

\int + (1 + x)^{3} d x

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

Schritte zur Lösung

\int (1 + x)^{3} d x

Multipliziere aus

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

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

\int 1 d x = x

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

\frac{\partial}{\partial x} (x e^{x} sin (y))

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

d er i v a t i v e (x^{3} - 12 x) (3 x^{2} + 2 x)

\frac{d}{d x} ((2^{x} \cdot x^{- 2})^{3 x - 1})

(3 x e^{x})^{^{'}}