∫ (x^2-2x-5) wrt x= eching

$$\int ( x ^ { 2 } - 2 x - 5 ) d x =$$

Baholash

$$\frac{x^{3}}{3}-x^{2}-5x+С$$

Yechim qadamlari

Summani muddatma-muddat integratsiya qiling.

$$\int x^{2}\mathrm{d}x+\int -2x\mathrm{d}x+\int -5\mathrm{d}x$$

Har bir shartda konstantani qavsdan tashqariga oling.

$$\int x^{2}\mathrm{d}x-2\int x\mathrm{d}x+\int -5\mathrm{d}x$$

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.

$$\frac{x^{3}}{3}-2\int x\mathrm{d}x+\int -5\mathrm{d}x$$

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

$$\frac{x^{3}}{3}-x^{2}+\int -5\mathrm{d}x$$

\int a\mathrm{d}x=ax umumiy integrallar qoidasi jadvalidan foydalanib, -5 integralini toping.

$$\frac{x^{3}}{3}-x^{2}-5x$$

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.

$$\frac{x^{3}}{3}-x^{2}-5x+С$$

x ga nisbatan hosilani topish

$$x^{2}-2x-5$$