展开 3(x^2-ln(2x))^2(2x-1/x)

解答

展开

3 (x^{2} - ln (2 x))^{2} (2 x - \frac{1}{x})

6 x^{5} - 12 x^{3} ln (2 x) + 6 x ln^{2} (2 x) - 3 x^{3} + 6 x ln (2 x) - \frac{3 ln ^{2} ( 2 x )}{x}

求解步骤

3 (x^{2} - ln (2 x))^{2} (2 x - \frac{1}{x})

使用分配律:

a (b - c) = ab - a c

a = 3 (x^{2} - ln (2 x))^{2}, b = 2 x, c = \frac{1}{x}

= 3 (x^{2} - ln (2 x))^{2} \cdot 2 x - 3 (x^{2} - ln (2 x))^{2} \frac{1}{x}

= 3 \cdot 2 x (x^{2} - ln (2 x))^{2} - 3 \cdot \frac{1}{x} (x^{2} - ln (2 x))^{2}

化简

3 \cdot 2 x (x^{2} - ln (2 x))^{2} - 3 \cdot \frac{1}{x} (x^{2} - ln (2 x))^{2} : 6 x^{5} - 12 x^{3} ln (2 x) + 6 x ln^{2} (2 x) - 3 x^{3} + 6 x ln (2 x) - \frac{3 ln ^{2} ( 2 x )}{x}

= 6 x^{5} - 12 x^{3} ln (2 x) + 6 x ln^{2} (2 x) - 3 x^{3} + 6 x ln (2 x) - \frac{3 ln ^{2} ( 2 x )}{x}

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

e x p an d (- 1, 2) y (4, - 2)

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

e x p an d - \frac{6 ( x + 1 ) ( x - 3 )}{3 - 2 x}

e x p an d \frac{( y + 1 ) ^{2}}{9}