展開する 2uy^2(ydu+udy)+(y^2-3y^2v^2)du

解

展開する

2 u y^{2} (y d u + u d y) + (y^{2} - 3 y^{2} v^{2}) d u

2 u y^{3} d u + 2 u^{2} y^{2} d y + y^{2} d u - 3 v^{2} y^{2} d u

解答ステップ

2 u y^{2} (y d u + u d y) + (y^{2} - 3 y^{2} v^{2}) d u

= 2 u y^{2} (y d u + u d y) + (y^{2} - 3 v^{2} y^{2}) d u

拡張

2 u y^{2} (y d u + u d y) : 2 u y^{3} d u + 2 u^{2} y^{2} d y

= 2 u y^{3} d u + 2 u^{2} y^{2} d y + (y^{2} - 3 y^{2} v^{2}) d u

拡張

d u (y^{2} - 3 y^{2} v^{2}) : y^{2} d u - 3 v^{2} y^{2} d u

= 2 u y^{3} d u + 2 u^{2} y^{2} d y + y^{2} d u - 3 v^{2} y^{2} d u