integral of x(x+2)^5

Lösung

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

\frac{x ^{7}}{7} + \frac{5 x ^{6}}{3} + 8 x^{5} + 20 x^{4} + \frac{80 x ^{3}}{3} + 16 x^{2} + C

Schritte zur Lösung

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

Multipliziere aus

x (x + 2)^{5} : x^{6} + 10 x^{5} + 40 x^{4} + 80 x^{3} + 80 x^{2} + 32 x

= \int x^{6} + 10 x^{5} + 40 x^{4} + 80 x^{3} + 80 x^{2} + 32 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^{6} d x + \int 10 x^{5} d x + \int 40 x^{4} d x + \int 80 x^{3} d x + \int 80 x^{2} d x + \int 32 x d x

\int x^{6} d x = \frac{x ^{7}}{7}

\int 10 x^{5} d x = \frac{5 x ^{6}}{3}

\int 40 x^{4} d x = 8 x^{5}

\int 80 x^{3} d x = 20 x^{4}

\int 80 x^{2} d x = \frac{80 x ^{3}}{3}

\int 32 x d x = 16 x^{2}

= \frac{x ^{7}}{7} + \frac{5 x ^{6}}{3} + 8 x^{5} + 20 x^{4} + \frac{80 x ^{3}}{3} + 16 x^{2}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{7}}{7} + \frac{5 x ^{6}}{3} + 8 x^{5} + 20 x^{4} + \frac{80 x ^{3}}{3} + 16 x^{2} + C

d er i v a t i v e f (x) = 4 arcsin (x^{4})

\frac{d}{d x} (\frac{x ^{2}}{x - 11})

d er i v a t i v e 3 x + \frac{4}{x}

\int_{2}^{3} \frac{19}{3 - x} d x

\frac{d}{d x} (x ln (x y))