integral of x(x-2)(x-4)

Lösung

\int x (x - 2) (x - 4) d x

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

Schritte zur Lösung

\int x (x - 2) (x - 4) d x

Multipliziere aus

x (x - 2) (x - 4) : x^{3} - 6 x^{2} + 8 x

= \int x^{3} - 6 x^{2} + 8 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 6 x^{2} d x + \int 8 x d x

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

\int 6 x^{2} d x = 2 x^{3}

\int 8 x d x = 4 x^{2}

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

Füge eine Konstante zur Lösung hinzu

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

\int (\frac{1}{2 - 3 x}) d x

\int 4 x^{5} 2 x^{2} + 3 d x

\int \frac{2 x sin ( x )}{cos ^{3} ( x )} d x

\int \frac{x ^{2} + 49}{x ^{4}} d x

\int \frac{x + 1}{3 x + 1} d x