Réitigh ∫ x^3+x^2-2x wrt x

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

Luacháil

$$\frac{x^{4}}{4}+\frac{x^{3}}{3}-x^{2}+С$$

Céimeanna Réitigh

Measc an tsuim téarma fá téarma.

$$\int x^{3}\mathrm{d}x+\int x^{2}\mathrm{d}x+\int -2x\mathrm{d}x$$

Fág an leanúnach sna téarmaí as an áireamh.

$$\int x^{3}\mathrm{d}x+\int x^{2}\mathrm{d}x-2\int x\mathrm{d}x$$

Ó \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} fá choinne k\neq -1, athchuir \int x^{3}\mathrm{d}x le \frac{x^{4}}{4}.

$$\frac{x^{4}}{4}+\int x^{2}\mathrm{d}x-2\int x\mathrm{d}x$$

Ó \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} fá choinne k\neq -1, athchuir \int x^{2}\mathrm{d}x le \frac{x^{3}}{3}.

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

Ó \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} fá choinne k\neq -1, athchuir \int x\mathrm{d}x le \frac{x^{2}}{2}. Méadaigh -2 faoi \frac{x^{2}}{2}.

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

Má tá F\left(x\right) mar frithdhíorthach do f\left(x\right), beidh tacar do frithdhíorthach uile do f\left(x\right) a thabhairt ag F\left(x\right)+C. Mar sin de, cur an comhtháthú leanúnach C\in \mathrm{R} don toradh.

$$\frac{x^{4}}{4}+\frac{x^{3}}{3}-x^{2}+С$$

Difreálaigh w.r.t. x

$$x\left(x-1\right)\left(x+2\right)$$