integral of (3x^2-9x+2)

Lösung

\int (3 x^{2} - 9 x + 2) d x

x^{3} - \frac{9 x ^{2}}{2} + 2 x + C

Schritte zur Lösung

\int 3 x^{2} - 9 x + 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 3 x^{2} d x - \int 9 x d x + \int 2 d x

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

\int 9 x d x = \frac{9 x ^{2}}{2}

\int 2 d x = 2 x

= x^{3} - \frac{9 x ^{2}}{2} + 2 x

Füge eine Konstante zur Lösung hinzu

= x^{3} - \frac{9 x ^{2}}{2} + 2 x + C

\int \frac{1 + cos ( x )}{1 - cos ( x )} d x

\frac{d}{d x} (arcsin (5 x))

d er i v a t i v e \frac{3}{5} x^{\frac{5}{3}} - \frac{3}{4} x^{\frac{1}{3}} + 9

x \to - 2 + lim (\frac{1 - x}{x ^{3} + 8})

x \to 1 - lim (\frac{2}{x - 1})