∫ x^2dive^2x wrt x eching

$$\int{ { x }^{ 2 } \div { e }^{ 2 } x }d x$$

Baholash

$$\frac{x^{4}}{4e^{2}}+С$$

Yechim qadamlari

\frac{x^{2}}{e^{2}}x ni yagona kasrga aylantiring.

$$\int \frac{x^{2}x}{e^{2}}\mathrm{d}x$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 2 va 1 ni qo‘shib, 3 ni oling.

$$\int \frac{x^{3}}{e^{2}}\mathrm{d}x$$

\int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x yordamidan konstantani qavsdan tashqariga chiqaring.

$$\frac{\int x^{3}\mathrm{d}x}{e^{2}}$$

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.

$$\frac{x^{4}}{4e^{2}}$$

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.

$$\frac{x^{4}}{4e^{2}}+С$$

x ga nisbatan hosilani topish

$$\frac{x^{3}}{e^{2}}$$