integral of (x^{3/2}+4x+3)

Lösung

\int (x^{\frac{3}{2}} + 4 x + 3) d x

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

Schritte zur Lösung

\int x^{\frac{3}{2}} + 4 x + 3 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^{\frac{3}{2}} d x + \int 4 x d x + \int 3 d x

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

\int 4 x d x = 2 x^{2}

\int 3 d x = 3 x

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

Füge eine Konstante zur Lösung hinzu

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

d er i v a t i v e 5 t + 6 t^{5}

\frac{d}{d x} (x (1 - x))

y^{^{'}} + 2 y = 0

x \to \infty lim (7 + \frac{6}{x})

im pl i c i t \frac{d y}{d x}, y = \frac{1}{x}