integral of (2x^3+x)(x^4+x^2)

Lösung

\int (2 x^{3} + x) (x^{4} + x^{2}) d x

\frac{x ^{8}}{4} + \frac{x ^{6}}{2} + \frac{x ^{4}}{4} + C

Schritte zur Lösung

\int (2 x^{3} + x) (x^{4} + x^{2}) d x

Multipliziere aus

(2 x^{3} + x) (x^{4} + x^{2}) : 2 x^{7} + 3 x^{5} + x^{3}

= \int 2 x^{7} + 3 x^{5} + 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 2 x^{7} d x + \int 3 x^{5} d x + \int x^{3} d x

\int 2 x^{7} d x = \frac{x ^{8}}{4}

\int 3 x^{5} d x = \frac{x ^{6}}{2}

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

= \frac{x ^{8}}{4} + \frac{x ^{6}}{2} + \frac{x ^{4}}{4}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{8}}{4} + \frac{x ^{6}}{2} + \frac{x ^{4}}{4} + C

d er i v a t i v e f (x) = - 2 x + 7

\int 7 x^{9} - 3 x^{6} + 10 x^{3} d x

x \to 0 lim (\frac{e ^{b x} - 1}{x})

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

x \to 0 lim (\frac{x - 6}{x - 2})