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

Lösung

\int (x + 1) (x + 3) d x

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

Schritte zur Lösung

\int (x + 1) (x + 3) d x

Multipliziere aus

(x + 1) (x + 3) : x^{2} + 4 x + 3

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

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

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

\int 3 d x = 3 x

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

Füge eine Konstante zur Lösung hinzu

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

in v erse l a pl a ce \frac{- 0.1 s}{s ^{2} - 9.8}

d er i v a t i v e y = \frac{4}{3} (x + 1)^{\frac{3}{2}}

\int_{0}^{- 0.5} 150 x d x

d er i v a t i v e (x^{2} + 5)^{2} (x - 5)

\int 6 x^{2} + 16 x - 10 d x