integral of 4x^5-2x^3+x-2

Lösung

\int 4 x^{5} - 2 x^{3} + x - 2 d x

\frac{2 x ^{6}}{3} - \frac{x ^{4}}{2} + \frac{x ^{2}}{2} - 2 x + C

Schritte zur Lösung

\int 4 x^{5} - 2 x^{3} + x - 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 4 x^{5} d x - \int 2 x^{3} d x + \int x d x - \int 2 d x

\int 4 x^{5} d x = \frac{2 x ^{6}}{3}

\int 2 x^{3} d x = \frac{x ^{4}}{2}

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

\int 2 d x = 2 x

= \frac{2 x ^{6}}{3} - \frac{x ^{4}}{2} + \frac{x ^{2}}{2} - 2 x

Füge eine Konstante zur Lösung hinzu

= \frac{2 x ^{6}}{3} - \frac{x ^{4}}{2} + \frac{x ^{2}}{2} - 2 x + C

\frac{d}{d x} (\frac{x - x ^{2}}{1 + 3 x ^{2}})

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

d er i v a t i v e f (x) = (3 x - 1) e^{- 6 x}

d er i v a t i v e \frac{y + 1}{y - 1}

x \to \infty lim (1^{x})