Réitigh ∫ 1.2x^2+16.2x+62.3 wrt x

$$\int 1.2 x ^ { 2 } + 16.2 x + 62.3 d x$$

Luacháil

$$\frac{2x^{3}}{5}+\frac{81x^{2}}{10}+\frac{623x}{10}+С$$

Céimeanna Réitigh

Measc an tsuim téarma fá téarma.

$$\int \frac{6x^{2}}{5}\mathrm{d}x+\int \frac{81x}{5}\mathrm{d}x+\int 62.3\mathrm{d}x$$

Fág an leanúnach sna téarmaí as an áireamh.

$$\frac{6\int x^{2}\mathrm{d}x}{5}+\frac{81\int x\mathrm{d}x}{5}+\int 62.3\mathrm{d}x$$

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}. Méadaigh 1.2 faoi \frac{x^{3}}{3}.

$$\frac{2x^{3}}{5}+\frac{81\int x\mathrm{d}x}{5}+\int 62.3\mathrm{d}x$$

Ó \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} fá choinne k\neq -1, athchuir \int x\mathrm{d}x le \frac{x^{2}}{2}. Méadaigh 16.2 faoi \frac{x^{2}}{2}.

$$\frac{2x^{3}}{5}+\frac{81x^{2}}{10}+\int 62.3\mathrm{d}x$$

Aimsigh suimeálaithe do 62.3 ag baint úsáid as an tábla do suimeálaithe coitianta riail\int a\mathrm{d}x=ax.

$$\frac{2x^{3}}{5}+\frac{81x^{2}}{10}+\frac{623x}{10}$$

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.

$$\frac{2x^{3}}{5}+\frac{81x^{2}}{10}+\frac{623x}{10}+С$$

Difreálaigh w.r.t. x

$$\frac{6x^{2}}{5}+\frac{81x}{5}+62.3$$