Réitigh ∫ esqrt{x wrt x=

$$\int{ e \sqrt{ x } }d x =$$

Luacháil

$$\frac{2ex^{\frac{3}{2}}}{3}+С$$

Céimeanna Réitigh

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.

$$e\int \sqrt{x}\mathrm{d}x$$

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.

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

Simpligh.

$$\frac{2ex^{\frac{3}{2}}}{3}$$

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.

$$\frac{2ex^{\frac{3}{2}}}{3}+С$$

Difreálaigh w.r.t. x

$$e\sqrt{x}$$