∫ (x^2/2-2/x^2) wrt x=x^3/6+2/x+c eching

$$\int ( \frac { x ^ { 2 } } { 2 } - \frac { 2 } { x ^ { 2 } } ) d x = \frac { x ^ { 3 } } { 6 } + \frac { 2 } { x } + c$$

c uchun yechish

$$c=С$$

$$x\neq 0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini 6x ga, 6,x ning eng kichik karralisiga ko‘paytiring.

$$6x\int \frac{x^{2}}{2}-\frac{2}{x^{2}}\mathrm{d}x=xx^{3}+6\times 2+6xc$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 1 va 3 ni qo‘shib, 4 ni oling.

$$6x\int \frac{x^{2}}{2}-\frac{2}{x^{2}}\mathrm{d}x=x^{4}+6\times 2+6xc$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 2 va x^{2} ning eng kichik umumiy karralisi 2x^{2}. \frac{x^{2}}{2} ni \frac{x^{2}}{x^{2}} marotabaga ko'paytirish. \frac{2}{x^{2}} ni \frac{2}{2} marotabaga ko'paytirish.

$$6x\int \frac{x^{2}x^{2}}{2x^{2}}-\frac{2\times 2}{2x^{2}}\mathrm{d}x=x^{4}+6\times 2+6xc$$

\frac{x^{2}x^{2}}{2x^{2}} va \frac{2\times 2}{2x^{2}} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$6x\int \frac{x^{2}x^{2}-2\times 2}{2x^{2}}\mathrm{d}x=x^{4}+6\times 2+6xc$$

x^{2}x^{2}-2\times 2 ichidagi ko‘paytirishlarni bajaring.

$$6x\int \frac{x^{4}-4}{2x^{2}}\mathrm{d}x=x^{4}+6\times 2+6xc$$

12 hosil qilish uchun 6 va 2 ni ko'paytirish.

$$6x\int \frac{x^{4}-4}{2x^{2}}\mathrm{d}x=x^{4}+12+6xc$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{4}+12+6xc=6x\int \frac{x^{4}-4}{2x^{2}}\mathrm{d}x$$

Ikkala tarafdan x^{4} ni ayirish.

$$12+6xc=6x\int \frac{x^{4}-4}{2x^{2}}\mathrm{d}x-x^{4}$$

Ikkala tarafdan 12 ni ayirish.

$$6xc=6x\int \frac{x^{4}-4}{2x^{2}}\mathrm{d}x-x^{4}-12$$

Tenglama standart shaklda.

$$6xc=Сx$$

Ikki tarafini 6x ga bo‘ling.

$$\frac{6xc}{6x}=\frac{Сx}{6x}$$

6x ga bo'lish 6x ga ko'paytirishni bekor qiladi.

$$c=\frac{Сx}{6x}$$

Сx ni 6x ga bo'lish.

$$c=\frac{С}{6}$$

x uchun yechish

$$x\neq 0$$

$$c=С\text{ and }x\neq 0$$