展開する (y+x(x^2+y^2)^2)dx+(y(x^2+y^2)^2-x)

解

展開する

(y + x (x^{2} + y^{2})^{2}) d x + (y (x^{2} + y^{2})^{2} - x)

y d x + x^{5} d x + 2 y^{2} x^{3} d x + y^{4} x d x + y x^{4} + 2 y^{3} x^{2} + y^{5} - x

解答ステップ

(y + x (x^{2} + y^{2})^{2}) d x + (y (x^{2} + y^{2})^{2} - x)

拡張

d x (y + x (x^{2} + y^{2})^{2}) : y d x + x^{5} d x + 2 y^{2} x^{3} d x + y^{4} x d x

= y d x + x^{5} d x + 2 y^{2} x^{3} d x + y^{4} x d x + (y (x^{2} + y^{2})^{2} - x)

簡素化

y d x + x^{5} d x + 2 y^{2} x^{3} d x + y^{4} x d x + (y (x^{2} + y^{2})^{2} - x) : y d x + x^{5} d x + 2 y^{2} x^{3} d x + y^{4} x d x + y x^{4} + 2 y^{3} x^{2} + y^{5} - x

= y d x + x^{5} d x + 2 y^{2} x^{3} d x + y^{4} x d x + y x^{4} + 2 y^{3} x^{2} + y^{5} - x