integral of (x+1)(x+3)^2

Lösung

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

\frac{x ^{4}}{4} + \frac{7 x ^{3}}{3} + \frac{15 x ^{2}}{2} + 9 x + C

Schritte zur Lösung

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

Multipliziere aus

(x + 1) (x + 3)^{2} : x^{3} + 7 x^{2} + 15 x + 9

= \int x^{3} + 7 x^{2} + 15 x + 9 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^{3} d x + \int 7 x^{2} d x + \int 15 x d x + \int 9 d x

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

\int 7 x^{2} d x = \frac{7 x ^{3}}{3}

\int 15 x d x = \frac{15 x ^{2}}{2}

\int 9 d x = 9 x

= \frac{x ^{4}}{4} + \frac{7 x ^{3}}{3} + \frac{15 x ^{2}}{2} + 9 x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{4}}{4} + \frac{7 x ^{3}}{3} + \frac{15 x ^{2}}{2} + 9 x + C

\frac{d}{d x} (\frac{32}{x})

a re a - x^{2} + 9, 1.25 x + 3

y^{^{'}} - y = 9 t e^{2 t}, y (0) = 1

x \to 0 - lim (\frac{1}{x \cdot e ^{\frac{1}{x}}})

x \to 2 lim (3 x^{3} - 12 x - 4)