integral of sqrt(x^3)+\sqrt[3]{x^2}

Lösung

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

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

Schritte zur Lösung

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

y^{^{''}} - 4 y^{^{'}} + 4 y = 5 t^{- 1} e^{2 t}

\frac{d}{d x} (x^{e x})

\frac{\partial}{\partial x} (x^{2} (x - y)^{- 2})

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

d er i v a t i v e f (x) = (2 x^{2} + 1)