展开 (5x^2-10)^3xdx

解答

展开

(5 x^{2} - 10)^{3} x d x

125 x^{7} d x - 750 x^{5} d x + 1500 x^{3} d x - 1000 x d x

求解步骤

(5 x^{2} - 10)^{3} x d x

(5 x^{2} - 10)^{3} = 125 x^{6} - 750 x^{4} + 1500 x^{2} - 1000

= x (125 x^{6} - 750 x^{4} + 1500 x^{2} - 1000) d x

= x (125 x^{6} - 750 x^{4} + 1500 x^{2} - 1000) d x

打开括号

= x d x \cdot 125 x^{6} + x d x (- 750 x^{4}) + x d x \cdot 1500 x^{2} + x d x (- 1000)

使用加减运算法则

+ (- a) = - a

= 125 x^{6} x d x - 750 x^{4} x d x + 1500 x^{2} x d x - 1000 x d x

化简

125 x^{6} x d x - 750 x^{4} x d x + 1500 x^{2} x d x - 1000 x d x : 125 x^{7} d x - 750 x^{5} d x + 1500 x^{3} d x - 1000 x d x

= 125 x^{7} d x - 750 x^{5} d x + 1500 x^{3} d x - 1000 x d x

s im pl i f y (x - \frac{1}{3}) (x + \frac{1}{3})

e x p an d \frac{( x ^{9} + 5 x ^{5} - x ^{3} + 2021 )}{x ^{3} ( x ^{4} - 16 )}

e x p an d 5 (2 + 4)

e x p an d 8 x^{2} - (8 x + 1) ln (x)

e x p an d \frac{2 x + 1}{x ^{2} ( x + 1 )}