∫ 12x^2+162x+623 wrt x eching

$$\int{ 12 { x }^{ 2 } +162x+623 }d x$$

Baholash

$$4x^{3}+81x^{2}+623x+С$$

Yechim qadamlari

Summani muddatma-muddat integratsiya qiling.

$$\int 12x^{2}\mathrm{d}x+\int 162x\mathrm{d}x+\int 623\mathrm{d}x$$

Har bir shartda konstantani qavsdan tashqariga oling.

$$12\int x^{2}\mathrm{d}x+162\int x\mathrm{d}x+\int 623\mathrm{d}x$$

k\neq -1 uchun integral \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} boʻlgani uchun, \int x^{2}\mathrm{d}x integralni \frac{x^{3}}{3} bilan almashtiring. 12 ni \frac{x^{3}}{3} marotabaga ko'paytirish.

$$4x^{3}+162\int x\mathrm{d}x+\int 623\mathrm{d}x$$

k\neq -1 uchun integral \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} boʻlgani uchun, \int x\mathrm{d}x integralni \frac{x^{2}}{2} bilan almashtiring. 162 ni \frac{x^{2}}{2} marotabaga ko'paytirish.

$$4x^{3}+81x^{2}+\int 623\mathrm{d}x$$

\int a\mathrm{d}x=ax umumiy integrallar qoidasi jadvalidan foydalanib, 623 integralini toping.

$$4x^{3}+81x^{2}+623x$$

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.

$$4x^{3}+81x^{2}+623x+С$$

x ga nisbatan hosilani topish

$$12x^{2}+162x+623$$