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

Lösung

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

x^{3} - 3 x^{2} + 3 x + C

Schritte zur Lösung

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

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

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

\int 3 d x = 3 x

= x^{3} - 3 x^{2} + 3 x

Füge eine Konstante zur Lösung hinzu

= x^{3} - 3 x^{2} + 3 x + C

\int_{0}^{\frac{1}{4}} 5 arcsin (4 x) d x

\int \frac{6 x ^{3} + 5 x ^{2} - 47 x - 36}{x ^{2} - 9} d x

t a y l or 10 - x, 1

x \to - \infty lim (x^{4})

t an g e n t f (x) = 4 x^{3} + 3 x, at x = - 4, - 1