Réitigh ∫ x^2dive^2x wrt x

$$\int{ { x }^{ 2 } \div { e }^{ 2 } x }d x$$

Luacháil

$$\frac{x^{4}}{4e^{2}}+С$$

Céimeanna Réitigh

Scríobh \frac{x^{2}}{e^{2}}x mar chodán aonair.

$$\int \frac{x^{2}x}{e^{2}}\mathrm{d}x$$

Chun cumhachtaí den bhonn céanna a iolrú, suimigh a n-easpónaint. Suimigh 2 agus 1 chun 3 a bhaint amach.

$$\int \frac{x^{3}}{e^{2}}\mathrm{d}x$$

Fág an úsáid leanúnach do\int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x as an áireamh.

$$\frac{\int x^{3}\mathrm{d}x}{e^{2}}$$

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}.

$$\frac{x^{4}}{4e^{2}}$$

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.

$$\frac{x^{4}}{4e^{2}}+С$$

Difreálaigh w.r.t. x

$$\frac{x^{3}}{e^{2}}$$