integral of (5-2/3 x^2+3/4 x^3)

Lösung

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

5 x - \frac{2 x ^{3}}{9} + \frac{3 x ^{4}}{16} + C

Schritte zur Lösung

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

\int 5 d x = 5 x

\int \frac{2}{3} x^{2} d x = \frac{2 x ^{3}}{9}

\int \frac{3}{4} x^{3} d x = \frac{3 x ^{4}}{16}

= 5 x - \frac{2 x ^{3}}{9} + \frac{3 x ^{4}}{16}

Füge eine Konstante zur Lösung hinzu

= 5 x - \frac{2 x ^{3}}{9} + \frac{3 x ^{4}}{16} + C

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

y^{^{''}} - 2 y^{^{'}} + y = 14.5 e^{t}

\frac{d}{d x} (n^{x})

\int x (2 x + 5)^{8} d x

x \to 6 - lim (\frac{1}{x - 6})