integral of (sqrt(3)+sqrt(x))^2

Lösung

\int (3 + x)^{2} d x

3 x + \frac{4}{3} x^{\frac{3}{2}} + \frac{x ^{2}}{2} + C

Schritte zur Lösung

\int (3 + x)^{2} d x

Multipliziere aus

(3 + x)^{2} : 3 + 23 x + x

= \int 3 + 23 x + x 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 d x + \int 23 x d x + \int x d x

\int 3 d x = 3 x

\int 23 x d x = \frac{4}{3} x^{\frac{3}{2}}

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

= 3 x + \frac{4}{3} x^{\frac{3}{2}} + \frac{x ^{2}}{2}

Füge eine Konstante zur Lösung hinzu

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

d er i v a t i v e f (x) = - x^{2}

x \to 7 lim (\frac{3}{x - 7})

x \to 0 lim (\frac{3 x}{x ^{2} + 2 x})

t an g e n t \frac{2}{x}

\frac{\partial}{\partial x} (4 - x)