Réitigh ∫ 12x^2+162x+623 wrt x

$$\int{ 12 { x }^{ 2 } +162x+623 }d x$$

Luacháil

$$4x^{3}+81x^{2}+623x+С$$

Céimeanna Réitigh

Measc an tsuim téarma fá téarma.

$$\int 12x^{2}\mathrm{d}x+\int 162x\mathrm{d}x+\int 623\mathrm{d}x$$

Fág an leanúnach sna téarmaí as an áireamh.

$$12\int x^{2}\mathrm{d}x+162\int x\mathrm{d}x+\int 623\mathrm{d}x$$

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}. Méadaigh 12 faoi \frac{x^{3}}{3}.

$$4x^{3}+162\int x\mathrm{d}x+\int 623\mathrm{d}x$$

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 162 faoi \frac{x^{2}}{2}.

$$4x^{3}+81x^{2}+\int 623\mathrm{d}x$$

Aimsigh suimeálaithe do 623 ag baint úsáid as an tábla do suimeálaithe coitianta riail\int a\mathrm{d}x=ax.

$$4x^{3}+81x^{2}+623x$$

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.

$$4x^{3}+81x^{2}+623x+С$$

Difreálaigh w.r.t. x

$$12x^{2}+162x+623$$