integral of-3/2 x^2+3x^4-2

Lösung

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

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

Schritte zur Lösung

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

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

\int 3 x^{4} d x = \frac{3 x ^{5}}{5}

\int 2 d x = 2 x

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

Füge eine Konstante zur Lösung hinzu

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

\frac{d}{d x} (\frac{1}{2} sec (x) - \frac{1}{3} csc (x))

\frac{d}{d x} (14 x)

x \to 3 lim (2 x^{3} - 4 x^{2} + x - 7)

\frac{\partial}{\partial x} (tan (3 x^{2} + 2 x))

\int 4 3 x - 8 d x