integral of (x^2+24x^3)/x

Lösung

\int \frac{x ^{2} + 24 x ^{3}}{x} d x

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

Schritte zur Lösung

\int \frac{x ^{2} + 24 x ^{3}}{x} d x

Vereinfache

\frac{x ^{2} + 24 x ^{3}}{x} : x (24 x + 1)

= \int x (24 x + 1) d x

Multipliziere aus

x (24 x + 1) : 24 x^{2} + x

= \int 24 x^{2} + 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 24 x^{2} d x + \int x d x

\int 24 x^{2} d x = 8 x^{3}

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

= 8 x^{3} + \frac{x ^{2}}{2}

Füge eine Konstante zur Lösung hinzu

= 8 x^{3} + \frac{x ^{2}}{2} + C

\frac{d}{d x} (arcsinh (5 x^{3} - 4 x^{2} + 11))

t an g e n t f (x) = 2 x - 1 + \frac{6}{x}, at x = 2

\frac{\partial}{\partial x} (A (e^{2 x} + 2 e^{2 x} x))

t an g e n t (x^{2} + y^{2})^{3} = 8 x^{2} y^{2}, (1, 1)

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