Réitigh ∫ left(x+1right)^2 wrt x

$$\int{ { \left(x+1 \right) }^{ 2 } }d x$$

Luacháil

$$\frac{\left(x+1\right)^{3}}{3}+С$$

Céimeanna Réitigh

Úsáid an teoirim dhéthéarmach \left(a+b\right)^{2}=a^{2}+2ab+b^{2} chun \left(x+1\right)^{2} a leathnú.

$$\int x^{2}+2x+1\mathrm{d}x$$

Measc an tsuim téarma fá téarma.

$$\int x^{2}\mathrm{d}x+\int 2x\mathrm{d}x+\int 1\mathrm{d}x$$

Fág an leanúnach sna téarmaí as an áireamh.

$$\int x^{2}\mathrm{d}x+2\int x\mathrm{d}x+\int 1\mathrm{d}x$$

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}.

$$\frac{x^{3}}{3}+2\int x\mathrm{d}x+\int 1\mathrm{d}x$$

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}.

$$\frac{x^{3}}{3}+x^{2}+\int 1\mathrm{d}x$$

Aimsigh suimeálaithe do 1 ag baint úsáid as an tábla do suimeálaithe coitianta riail\int a\mathrm{d}x=ax.

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

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.

$$\frac{x^{3}}{3}+x^{2}+x+С$$

Difreálaigh w.r.t. x

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