Réitigh ∫ x-2sqrt{x}+1 wrt x

$$\int{ x-2 \sqrt{ x } +1 }d x$$

Luacháil

$$\frac{x^{2}}{2}-\frac{4x^{\frac{3}{2}}}{3}+x+С$$

Céimeanna Réitigh

Measc an tsuim téarma fá téarma.

$$\int x\mathrm{d}x+\int -2\sqrt{x}\mathrm{d}x+\int 1\mathrm{d}x$$

Fág an leanúnach sna téarmaí as an áireamh.

$$\int x\mathrm{d}x-2\int \sqrt{x}\mathrm{d}x+\int 1\mathrm{d}x$$

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}.

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

Athscríobh \sqrt{x} mar x^{\frac{1}{2}}. Ó \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} fá choinne k\neq -1, athchuir \int x^{\frac{1}{2}}\mathrm{d}x le \frac{x^{\frac{3}{2}}}{\frac{3}{2}}. Simpligh. Méadaigh -2 faoi \frac{2x^{\frac{3}{2}}}{3}.

$$\frac{x^{2}}{2}-\frac{4x^{\frac{3}{2}}}{3}+\int 1\mathrm{d}x$$

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

$$\frac{x^{2}}{2}-\frac{4x^{\frac{3}{2}}}{3}+x$$

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.

$$\frac{x^{2}}{2}-\frac{4x^{\frac{3}{2}}}{3}+x+С$$

Difreálaigh w.r.t. x

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