integral of x(1+2x^4)

Lösung

\int x (1 + 2 x^{4}) d x

\frac{x ^{2}}{2} + \frac{x ^{6}}{3} + C

Schritte zur Lösung

\int x (1 + 2 x^{4}) d x

Multipliziere aus

x (1 + 2 x^{4}) : x + 2 x^{5}

= \int x + 2 x^{5} 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 d x + \int 2 x^{5} d x

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

\int 2 x^{5} d x = \frac{x ^{6}}{3}

= \frac{x ^{2}}{2} + \frac{x ^{6}}{3}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{2}}{2} + \frac{x ^{6}}{3} + C

\frac{\partial}{\partial x} (4 x^{3} y^{2} + 3)

d er i v a t i v e y = ln (2 x + 1)

\frac{d}{d x} (lo g_{2} (2 x^{2} - 7 x + 1))

\int 4 x e^{9 x} d x

t an g e n t f (x) = x^{4} - 5 x^{2} - x, at x = 1