∫ x/2sqrt{x wrt x eching

$$\int \frac { x } { 2 \sqrt { x } } d x$$

Baholash

$$\frac{x^{\frac{3}{2}}}{3}+С$$

Yechim qadamlari

\frac{x}{2\sqrt{x}} ichida hali faktorlanmagan ifodalarni faktorlang.

$$\int \frac{x}{2\sqrt{x}}\mathrm{d}x$$

Surat va maxrajdagi ikkala \sqrt{x} ni qisqartiring.

$$\int \frac{\sqrt{x}}{2}\mathrm{d}x$$

\int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x yordamidan konstantani qavsdan tashqariga chiqaring.

$$\frac{\int \sqrt{x}\mathrm{d}x}{2}$$

\sqrt{x} ni x^{\frac{1}{2}} sifatida qaytadan yozish. k\neq -1 uchun integral \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} boʻlgani uchun, \int x^{\frac{1}{2}}\mathrm{d}x integralni \frac{x^{\frac{3}{2}}}{\frac{3}{2}} bilan almashtiring. Qisqartirish.

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

Агар F\left(x\right)f\left(x\right) ning dastlabki holati boʻlsa, u holatda f\left(x\right) ning barcha dastlabki holatlari toʻplami F\left(x\right)+C tarafidan belgilanadi. Shu sababli natijaga C\in \mathrm{R} integrallash konstantasini qoʻshing.

$$\frac{x^{\frac{3}{2}}}{3}+С$$

x ga nisbatan hosilani topish

$$\frac{\sqrt{x}}{2}$$