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

f (x) = \frac{x cos ( x ) + π}{x - π}

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

\frac{\partial}{\partial x} ((ln (x))^{2})

\int \frac{x ^{3} + x ^{2} - x ^{5}}{x ^{6}} d x