∫ f(x) wrt x=f(x)dx eching

$$\int f ( x ) d x = f ( x ) d x$$

d uchun yechish

$$\left\{\begin{matrix}d=\frac{1}{2}+\frac{С}{2fx^{2}}\text{, }&x\neq 0\text{ and }f\neq 0\\d\in \mathrm{R}\text{, }&\left(x=0\text{ or }f=0\right)\text{ and }С=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$\int fx\mathrm{d}x=fx^{2}d$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$fx^{2}d=\int fx\mathrm{d}x$$

Tenglama standart shaklda.

$$fx^{2}d=\frac{fx^{2}}{2}+С$$

Ikki tarafini x^{2}f ga bo‘ling.

$$\frac{fx^{2}d}{fx^{2}}=\frac{\frac{fx^{2}}{2}+С}{fx^{2}}$$

x^{2}f ga bo'lish x^{2}f ga ko'paytirishni bekor qiladi.

$$d=\frac{\frac{fx^{2}}{2}+С}{fx^{2}}$$

\frac{fx^{2}}{2}+С ni x^{2}f ga bo'lish.

$$d=\frac{1}{2}+\frac{С}{fx^{2}}$$

f uchun yechish

$$\left\{\begin{matrix}f=\frac{С}{\left(1-d\right)x^{2}}\text{, }&d\neq 1\text{ and }x\neq 0\\f\in \mathrm{R}\text{, }&\left(x=0\text{ or }d=1\right)\text{ and }С=0\end{matrix}\right,$$