展开 (4x^2-3x)^4(8x-3)dx

解答

展开

(4 x^{2} - 3 x)^{4} (8 x - 3) d x

2048 x^{9} d x - 6912 x^{8} d x + 9216 x^{7} d x - 6048 x^{6} d x + 1944 x^{5} d x - 243 x^{4} d x

求解步骤

(4 x^{2} - 3 x)^{4} (8 x - 3) d x

使用分配律:

a (b - c) = ab - a c

a = (4 x^{2} - 3 x)^{4} d x, b = 8 x, c = 3

= (4 x^{2} - 3 x)^{4} d x \cdot 8 x - (4 x^{2} - 3 x)^{4} d x \cdot 3

= 8 x (4 x^{2} - 3 x)^{4} d x - 3 (4 x^{2} - 3 x)^{4} d x

化简

8 x (4 x^{2} - 3 x)^{4} d x - 3 (4 x^{2} - 3 x)^{4} d x : 2048 x^{9} d x - 6912 x^{8} d x + 9216 x^{7} d x - 6048 x^{6} d x + 1944 x^{5} d x - 243 x^{4} d x

= 2048 x^{9} d x - 6912 x^{8} d x + 9216 x^{7} d x - 6048 x^{6} d x + 1944 x^{5} d x - 243 x^{4} d x

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

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s im pl i f y (1 + cot (x)) (- csc^{2} (x))

e x p an d \frac{( 24 a + 5 b ) ^{2}}{225}

e x p an d \frac{x ^{2} - 2015 x + 2014}{2015 ( x ^{2} + 2014 )}