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

Lösung

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

\frac{x ^{5}}{5} - \frac{x ^{4}}{2} + 2 x + C

Schritte zur Lösung

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

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

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

\int 2 d x = 2 x

= \frac{x ^{5}}{5} - \frac{x ^{4}}{2} + 2 x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{5}}{5} - \frac{x ^{4}}{2} + 2 x + C

\int 16 x^{3} cos (2 - x^{4}) d x

\frac{d}{d u} (cos (u))

y^{^{''}} + 2 y^{^{'}} + y = 0, y (0) = 4, y^{^{'}} (0) = - 3

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

x \to - 1 lim (8 x^{4} - 3 x^{3} + 7 x)