integral of x^3-6x^2+9x+6

Lösung

\int x^{3} - 6 x^{2} + 9 x + 6 d x

\frac{x ^{4}}{4} - 2 x^{3} + \frac{9 x ^{2}}{2} + 6 x + C

Schritte zur Lösung

\int x^{3} - 6 x^{2} + 9 x + 6 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 x^{3} d x - \int 6 x^{2} d x + \int 9 x d x + \int 6 d x

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

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

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

\int 6 d x = 6 x

= \frac{x ^{4}}{4} - 2 x^{3} + \frac{9 x ^{2}}{2} + 6 x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{4}}{4} - 2 x^{3} + \frac{9 x ^{2}}{2} + 6 x + C

\int \frac{14 x - 46}{( x - 2 ) ( x - 5 )} d x

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

\int \frac{e ^{5 x} - 2 e ^{4 x} - 1}{e ^{4 x}} d x

\int e^{- (x - 8)^{3}} (x - 8)^{2} d x

\int \frac{x ^{4} + x}{x ^{3} - x ^{2} + x - 1} d x