integral of 10x^3+2x^2+1/2 x+3

Lösung

\int 10 x^{3} + 2 x^{2} + \frac{1}{2} x + 3 d x

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

Schritte zur Lösung

\int 10 x^{3} + 2 x^{2} + \frac{1}{2} 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 10 x^{3} d x + \int 2 x^{2} d x + \int \frac{1}{2} x d x + \int 3 d x

\int 10 x^{3} d x = \frac{5 x ^{4}}{2}

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

\int \frac{1}{2} x d x = \frac{x ^{2}}{4}

\int 3 d x = 3 x

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

Füge eine Konstante zur Lösung hinzu

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

\frac{d y}{d x} = (y - 5)^{2}

\frac{d y}{d x}

d er i v a t i v e \frac{- 14 x}{12 y}

a re a y = \frac{1}{2} x^{2}, y = - x^{2} + 6

\int x \cdot ln (x - 1) d x