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

Lösung

\int (x + 1) (x + 2) d x

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

Schritte zur Lösung

\int (x + 1) (x + 2) d x

Multipliziere aus

(x + 1) (x + 2) : x^{2} + 3 x + 2

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

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

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

\int 2 d x = 2 x

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

Füge eine Konstante zur Lösung hinzu

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

x \to 1 lim (\frac{1}{x + 1})

a re a f (x) = x^{2}, x = 0, x = 2

d er i v a t i v e \frac{6 e ^{s} s - 5 e ^{s}}{( 6 s + 1 ) ^{2}}

\int \frac{x ^{3} + 22}{x ^{2} + 7 x + 12} d x

t an g e n t y = 3 e^{x} + x, (0, 3)