integral of (3x^2-4x+7)

Lösung

\int (3 x^{2} - 4 x + 7) d x

x^{3} - 2 x^{2} + 7 x + C

Schritte zur Lösung

\int 3 x^{2} - 4 x + 7 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 4 x d x + \int 7 d x

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

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

\int 7 d x = 7 x

= x^{3} - 2 x^{2} + 7 x

Füge eine Konstante zur Lösung hinzu

= x^{3} - 2 x^{2} + 7 x + C

d er i v a t i v e f (x) = (\frac{x ^{2} + 4}{x ^{2} - 4})^{4}

\frac{d y}{d x} = \frac{( x y + 3 x - y - 3 )}{( x y - 2 x + 4 y - 8 )}

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

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

x \to \infty lim (\frac{( 25 x + 7 ) 5 x ^{2} + 2}{5 x ^{2} + 2})