∫ x^8(5x-3) wrt x eching

$$\int x ^ { 8 } ( 5 x - 3 ) d x$$

Baholash

$$\frac{x^{10}}{2}-\frac{x^{9}}{3}+С$$

Yechim qadamlari

x^{8} ga 5x-3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\int 5x^{9}-3x^{8}\mathrm{d}x$$

Summani muddatma-muddat integratsiya qiling.

$$\int 5x^{9}\mathrm{d}x+\int -3x^{8}\mathrm{d}x$$

Har bir shartda konstantani qavsdan tashqariga oling.

$$5\int x^{9}\mathrm{d}x-3\int x^{8}\mathrm{d}x$$

k\neq -1 uchun integral \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} boʻlgani uchun, \int x^{9}\mathrm{d}x integralni \frac{x^{10}}{10} bilan almashtiring. 5 ni \frac{x^{10}}{10} marotabaga ko'paytirish.

$$\frac{x^{10}}{2}-3\int x^{8}\mathrm{d}x$$

k\neq -1 uchun integral \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} boʻlgani uchun, \int x^{8}\mathrm{d}x integralni \frac{x^{9}}{9} bilan almashtiring. -3 ni \frac{x^{9}}{9} marotabaga ko'paytirish.

$$\frac{x^{10}}{2}-\frac{x^{9}}{3}$$

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.

$$\frac{x^{10}}{2}-\frac{x^{9}}{3}+С$$

x ga nisbatan hosilani topish

$$\left(5x-3\right)x^{8}$$