展开 uy^2(udy+ydu)

解答

展开

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

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

求解步骤

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

使用分配律:

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

化简

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

e x p an d 1 0^{30} (y^{30} + 2729079 y^{20}) d y

e x p an d y^{2} (y^{3} - ln (x))

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

e x p an d π (8 ln (3) - \frac{8}{3})

s im pl i f y 1 + \frac{10 ( 0.5 s + 1 )}{s ( 2 s + 1 )}