What is expand (y^2e^{xy^2}+4x^3)dx ?

The solution to expand (y^2e^{xy^2}+4x^3)dx is e^{y^2x}y^2dx+4x^3dx

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expand (y^2e^{xy^2}+4x^3)dx

expand

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

e^{y^{2} x} y^{2} d x + 4 x^{3} d x

Solution steps

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

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

Apply the distributive law:

a (b + c) = ab + a c

a = d x, b = y^{2} e^{x y^{2}}, c = 4 x^{3}

= d x y^{2} e^{x y^{2}} + d x \cdot 4 x^{3}

= e^{y^{2} x} y^{2} d x + 4 x^{3} d x

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What is expand (y^2e^{xy^2}+4x^3)dx ?
The solution to expand (y^2e^{xy^2}+4x^3)dx is e^{y^2x}y^2dx+4x^3dx