展开 y(y^2+1)dx

解答

展开

y (y^{2} + 1) d x

y^{3} d x + y d x

求解步骤

y (y^{2} + 1) d x

使用分配律:

a (b + c) = ab + a c

a = y d x, b = y^{2}, c = 1

= y d x y^{2} + y d x \cdot 1

= y^{2} y d x + 1 \cdot y d x

化简

y^{2} y d x + 1 \cdot y d x : y^{3} d x + y d x

= y^{3} d x + y d x

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e x p an d (4 x^{3} + 1) d x