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

Lösung

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

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

Schritte zur Lösung

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

Multipliziere aus

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

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

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

\int - \frac{1}{2 e ^{2 x}} d x

\int (2 - x)^{4} d x

\int 5 x (x^{2} + 6) d x

\int e^{7 - 2 x} d x

\int + se x^{2} x d x