integral of (6x^6-6x^5-4x^3+2)

Lösung

\int (6 x^{6} - 6 x^{5} - 4 x^{3} + 2) d x

\frac{6 x ^{7}}{7} - x^{6} - x^{4} + 2 x + C

Schritte zur Lösung

\int 6 x^{6} - 6 x^{5} - 4 x^{3} + 2 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 6 x^{6} d x - \int 6 x^{5} d x - \int 4 x^{3} d x + \int 2 d x

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

\int 6 x^{5} d x = x^{6}

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

\int 2 d x = 2 x

= \frac{6 x ^{7}}{7} - x^{6} - x^{4} + 2 x

Füge eine Konstante zur Lösung hinzu

= \frac{6 x ^{7}}{7} - x^{6} - x^{4} + 2 x + C

t a y l or ln (cos (x)), 0

\frac{d}{d x} ((x + 5)^{\frac{2}{3}})

\frac{d y}{d x} = (x + y - 2)^{2}

d er i v a t i v e y = \frac{C}{x}

\int (\frac{1}{x} - \frac{2}{x ^{2}} + \frac{5}{x ^{3}}) d x