integral of 3-1(x^3-2x^2+x+1)

Lösung

\int 3 - 1 (x^{3} - 2 x^{2} + x + 1) d x

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

Schritte zur Lösung

\int 3 - 1 \cdot (x^{3} - 2 x^{2} + x + 1) d x

Vereinfache

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

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

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

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

\int 2 d x = 2 x

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

Füge eine Konstante zur Lösung hinzu

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

\int r^{2} (\frac{r ^{3}}{21} + 3)^{6} d r

\int \frac{5}{3 s ^{2} + 1} d s

\int (2 + \frac{1}{x}) d x

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

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