Réitigh ∫ x^2-x^3 wrt x

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

Luacháil

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

Céimeanna Réitigh

Measc an tsuim téarma fá téarma.

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

Fág an leanúnach sna téarmaí as an áireamh.

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

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}.

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

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}. Méadaigh -1 faoi \frac{x^{4}}{4}.

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

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.

$$\frac{x^{3}}{3}-\frac{x^{4}}{4}+С$$

Difreálaigh w.r.t. x

$$\left(1-x\right)x^{2}$$