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

Lösung

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

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

Schritte zur Lösung

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

\frac{d}{d x} (arcsin (2 x))

\frac{\partial}{\partial x} (y ln (x))

\int 12 t^{3} d t

\frac{\partial}{\partial x} (x^{2} y + x y^{2} + 20)

\frac{d}{d x} (x^{0.7} y^{0.3})