integral of 3x^3-5x^2+7x+2

Lösung

\int 3 x^{3} - 5 x^{2} + 7 x + 2 d x

\frac{3 x ^{4}}{4} - \frac{5 x ^{3}}{3} + \frac{7 x ^{2}}{2} + 2 x + C

Schritte zur Lösung

\int 3 x^{3} - 5 x^{2} + 7 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^{3} d x - \int 5 x^{2} d x + \int 7 x d x + \int 2 d x

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

\int 5 x^{2} d x = \frac{5 x ^{3}}{3}

\int 7 x d x = \frac{7 x ^{2}}{2}

\int 2 d x = 2 x

= \frac{3 x ^{4}}{4} - \frac{5 x ^{3}}{3} + \frac{7 x ^{2}}{2} + 2 x

Füge eine Konstante zur Lösung hinzu

= \frac{3 x ^{4}}{4} - \frac{5 x ^{3}}{3} + \frac{7 x ^{2}}{2} + 2 x + C

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

x \to \infty lim (\frac{3 x ^{2} + 2 x - 8}{4 x ^{4} - 5 x + 4})

x \to 0 lim (\frac{1}{x + 1})

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

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