∫ int{x^2left(x^2+y^2right)^3 wrt x}dA8 eching

$$\int{ \int{ { x }^{ 2 } { \left( { x }^{ 2 } + { y }^{ 2 } \right) }^{ 3 } }d x }d A 8$$

Baholash

$$A_{8}\left(\frac{x^{3}y^{6}}{3}+\frac{3y^{2}x^{7}}{7}+\frac{3y^{4}x^{5}}{5}+\frac{x^{9}}{9}\right)+СA_{8}+С_{1}$$

Yechim qadamlari

\int a\mathrm{d}A_{8}=aA_{8} umumiy integrallar qoidasi jadvalidan foydalanib, \int x^{2}\left(x^{2}+y^{2}\right)^{3}\mathrm{d}x integralini toping.

$$\int x^{2}\left(x^{2}+y^{2}\right)^{3}\mathrm{d}xA_{8}$$

Qisqartirish.

$$\left(\frac{y^{6}x^{3}}{3}+\frac{3y^{4}x^{5}}{5}+\frac{3y^{2}x^{7}}{7}+\frac{x^{9}}{9}+С\right)A_{8}$$

Агар F\left(A_{8}\right)f\left(A_{8}\right) ning dastlabki holati boʻlsa, u holatda f\left(A_{8}\right) ning barcha dastlabki holatlari toʻplami F\left(A_{8}\right)+C tarafidan belgilanadi. Shu sababli natijaga C\in \mathrm{R} integrallash konstantasini qoʻshing.

$$\left(\frac{y^{6}x^{3}}{3}+\frac{3y^{4}x^{5}}{5}+\frac{3y^{2}x^{7}}{7}+\frac{x^{9}}{9}+С\right)A_{8}+С$$

x ga nisbatan hosilani topish

$$A_{8}x^{2}\left(x^{2}+y^{2}\right)^{3}$$