展开 vx(x^2+vx^2-2v^2x^2)dx

解答

展开

vx (x^{2} + v x^{2} - 2 v^{2} x^{2}) d x

v x^{3} d x + v^{2} x^{3} d x - 2 v^{3} x^{3} d x

求解步骤

vx (x^{2} + v x^{2} - 2 v^{2} x^{2}) d x

打开括号

= vx d x x^{2} + vx d xv x^{2} + vx d x (- 2 v^{2} x^{2})

使用加减运算法则

+ (- a) = - a

= v x^{2} x d x + vv x^{2} x d x - 2 v^{2} v x^{2} x d x

化简

v x^{2} x d x + vv x^{2} x d x - 2 v^{2} v x^{2} x d x : v x^{3} d x + v^{2} x^{3} d x - 2 v^{3} x^{3} d x

= v x^{3} d x + v^{2} x^{3} d x - 2 v^{3} x^{3} d x

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

e x p an d 2 - (4 (- 2) \cdot 5)

e x p an d \frac{RT V - a}{V ( V - b )}

e x p an d 52 e^{4 x} - 4 (13 e^{4 t} - 11)

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