展开 (1-3x)^9dx

解答

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(1 - 3 x)^{9} d x

d x - 27 x d x + 324 x^{2} d x - 2268 x^{3} d x + 10206 x^{4} d x - 30618 x^{5} d x + 61236 x^{6} d x - 78732 x^{7} d x + 59049 x^{8} d x - 19683 x^{9} d x

求解步骤

(1 - 3 x)^{9} d x

(1 - 3 x)^{9} = 1 - 27 x + 324 x^{2} - 2268 x^{3} + 10206 x^{4} - 30618 x^{5} + 61236 x^{6} - 78732 x^{7} + 59049 x^{8} - 19683 x^{9}

= (- 19683 x^{9} + 59049 x^{8} - 78732 x^{7} + 61236 x^{6} - 30618 x^{5} + 10206 x^{4} - 2268 x^{3} + 324 x^{2} - 27 x + 1) d x

打开括号

= d x \cdot 1 + d x (- 27 x) + d x \cdot 324 x^{2} + d x (- 2268 x^{3}) + d x \cdot 10206 x^{4} + d x (- 30618 x^{5}) + d x \cdot 61236 x^{6} + d x (- 78732 x^{7}) + d x \cdot 59049 x^{8} + d x (- 19683 x^{9})

使用加减运算法则

+ (- a) = - a

= 1 \cdot d x - 27 x d x + 324 x^{2} d x - 2268 x^{3} d x + 10206 x^{4} d x - 30618 x^{5} d x + 61236 x^{6} d x - 78732 x^{7} d x + 59049 x^{8} d x - 19683 x^{9} d x

乘以:

1 \cdot d x = d x

= d x - 27 x d x + 324 x^{2} d x - 2268 x^{3} d x + 10206 x^{4} d x - 30618 x^{5} d x + 61236 x^{6} d x - 78732 x^{7} d x + 59049 x^{8} d x - 19683 x^{9} d x

e x p an d 2 (x + 2 - 2 ln (x + 2)) + c

e x p an d 0 ((1, 1, 2) + (3, - 2, 0))

e x p an d \frac{4 ( x - 4 ) ( x + 6 )}{x}

e x p an d \frac{6}{45}

e x p an d ln (y) (1 - a)