展开 (ye^y-xe^x)dx

解答

展开

(y e^{y} - x e^{x}) d x

e^{y} y d x - e^{x} x d x

求解步骤

(y e^{y} - x e^{x}) d x

= (e^{y} y - e^{x} x) d x

使用分配律:

a (b - c) = ab - a c

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

= d x y e^{y} - d xx e^{x}

= e^{y} y d x - e^{x} x d x

e x p an d 2 y \cdot e^{2 x y} \cdot (x + y)^{2}

e x p an d x^{3} \cdot 2 x + 2 (2 x)^{2} - x^{3} \cdot x^{2} - 2 (x^{2})^{2}

e x p an d arcsin (\frac{1}{1.33})

e x p an d \frac{1}{4 a ( a - b )}

e x p an d 10 (\frac{1}{2} x + \frac{2}{5} y = 4)