∫ (6x^2+8x+3) wrt x eching

$$\int ( 6 x ^ { 2 } + 8 x + 3 ) d x$$

Baholash

$$2x^{3}+4x^{2}+3x+С$$

Yechim qadamlari

Summani muddatma-muddat integratsiya qiling.

$$\int 6x^{2}\mathrm{d}x+\int 8x\mathrm{d}x+\int 3\mathrm{d}x$$

Har bir shartda konstantani qavsdan tashqariga oling.

$$6\int x^{2}\mathrm{d}x+8\int x\mathrm{d}x+\int 3\mathrm{d}x$$

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. 6 ni \frac{x^{3}}{3} marotabaga ko'paytirish.

$$2x^{3}+8\int x\mathrm{d}x+\int 3\mathrm{d}x$$

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. 8 ni \frac{x^{2}}{2} marotabaga ko'paytirish.

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

\int a\mathrm{d}x=ax umumiy integrallar qoidasi jadvalidan foydalanib, 3 integralini toping.

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

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.

$$2x^{3}+4x^{2}+3x+С$$

x ga nisbatan hosilani topish

$$6x^{2}+8x+3$$