∫ x^2-x^3 wrt x eching

$$\int x ^ { 2 } - x ^ { 3 } d x$$

Baholash

$$-\frac{x^{4}}{4}+\frac{x^{3}}{3}+С$$

Yechim qadamlari

Summani muddatma-muddat integratsiya qiling.

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

Har bir shartda konstantani qavsdan tashqariga oling.

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

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.

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

k\neq -1 uchun integral \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} boʻlgani uchun, \int x^{3}\mathrm{d}x integralni \frac{x^{4}}{4} bilan almashtiring. -1 ni \frac{x^{4}}{4} marotabaga ko'paytirish.

$$\frac{x^{3}}{3}-\frac{x^{4}}{4}$$

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.

$$\frac{x^{3}}{3}-\frac{x^{4}}{4}+С$$

x ga nisbatan hosilani topish

$$\left(1-x\right)x^{2}$$