integral of (3x^4+x^2+2)

Lösung

\int (3 x^{4} + x^{2} + 2) d x

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

Schritte zur Lösung

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

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

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

\int 2 d x = 2 x

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

Füge eine Konstante zur Lösung hinzu

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

\frac{\partial}{\partial x} (12 x^{2} y^{5} + x^{2} y^{2})

x \to 0 lim (x^{4} f (x))

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

2 y (x + 1) d y = x d x

t a y l or \frac{1}{x ^{2}}, at 4