展开 (x^2+3x-1)^7(2x-3)dx

解答

展开

(x^{2} + 3 x - 1)^{7} (2 x - 3) d x

2 x^{15} d x + 39 x^{14} d x + 301 x^{13} d x + 1092 x^{12} d x + 1365 x^{11} d x - 2457 x^{10} d x - 8008 x^{9} d x - 897 x^{8} d x + 11401 x^{7} d x - 1365 x^{6} d x - 8736 x^{5} d x + 7371 x^{4} d x - 2821 x^{3} d x + 588 x^{2} d x - 65 x d x + 3 d x

求解步骤

(x^{2} + 3 x - 1)^{7} (2 x - 3) d x

使用分配律:

a (b - c) = ab - a c

a = (x^{2} + 3 x - 1)^{7} d x, b = 2 x, c = 3

= (x^{2} + 3 x - 1)^{7} d x \cdot 2 x - (x^{2} + 3 x - 1)^{7} d x \cdot 3

= 2 x (x^{2} + 3 x - 1)^{7} d x - 3 (x^{2} + 3 x - 1)^{7} d x

化简

2 x (x^{2} + 3 x - 1)^{7} d x - 3 (x^{2} + 3 x - 1)^{7} d x : 2 x^{15} d x + 39 x^{14} d x + 301 x^{13} d x + 1092 x^{12} d x + 1365 x^{11} d x - 2457 x^{10} d x - 8008 x^{9} d x - 897 x^{8} d x + 11401 x^{7} d x - 1365 x^{6} d x - 8736 x^{5} d x + 7371 x^{4} d x - 2821 x^{3} d x + 588 x^{2} d x - 65 x d x + 3 d x

= 2 x^{15} d x + 39 x^{14} d x + 301 x^{13} d x + 1092 x^{12} d x + 1365 x^{11} d x - 2457 x^{10} d x - 8008 x^{9} d x - 897 x^{8} d x + 11401 x^{7} d x - 1365 x^{6} d x - 8736 x^{5} d x + 7371 x^{4} d x - 2821 x^{3} d x + 588 x^{2} d x - 65 x d x + 3 d x

e x p an d lo g_{5} 3 \frac{( x + 9 ) ^{9}}{5}

e x p an d (cos (x) + cot (x))^{2}

s im pl i f y x (x^{2} + 2 x)

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

s im pl i f y 2 x^{2} - (1 + 23) x + 3