What is expand uy^2(udy+ydu) ?

The solution to expand uy^2(udy+ydu) is u^2y^2dy+uy^3du

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expand uy^2(udy+ydu)

expand

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

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

Solution steps

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

Apply the distributive law:

a (b + c) = ab + a c

a = u y^{2}, b = u d y, c = y d u

= u y^{2} u d y + u y^{2} y d u

= uu y^{2} d y + u y^{2} y d u

Simplify

uu y^{2} d y + u y^{2} y d u : u^{2} y^{2} d y + u y^{3} d u

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

1 0^{30} (y^{30} + 2729079 y^{20}) d y

y^{2} (y^{3} - ln (x))

x e^{(1 - x^{2} - y^{2})} - 2 e^{(1 - x^{2} - y^{2})} x (x + y)

π (8 ln (3) - \frac{8}{3})

1 + \frac{10 ( 0.5 s + 1 )}{s ( 2 s + 1 )}

What is expand uy^2(udy+ydu) ?
The solution to expand uy^2(udy+ydu) is u^2y^2dy+uy^3du