integral of (sqrt(x)+1)*(x-sqrt(x)+1)

Lösung

\int (x + 1) \cdot (x - x + 1) d x

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

Schritte zur Lösung

\int (x + 1) (x - x + 1) d x

Multipliziere aus

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

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

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

\int 1 d x = x

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

Füge eine Konstante zur Lösung hinzu

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

e^{x + y} d x + d y = 0

\frac{\partial}{\partial z} (4 y (z + 1)^{2})

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

x \to 3 - lim (k (x) (x - 5))

\frac{\partial}{\partial z} (e^{x y} + ln (2 x z) + sin (x^{2} y^{2}))