展开 (dx)/((x+2)(x^2+2x+4)^2)

解答

展开

\frac{d x}{( x + 2 ) ( x ^{2} + 2 x + 4 ) ^{2}}

\frac{d x}{x ^{5} + 6 x ^{4} + 20 x ^{3} + 40 x ^{2} + 48 x + 32}

求解步骤

\frac{d x}{( x + 2 ) ( x ^{2} + 2 x + 4 ) ^{2}}

(x^{2} + 2 x + 4)^{2} = x^{4} + 4 x^{3} + 12 x^{2} + 16 x + 16

= \frac{d x}{( x + 2 ) ( x ^{4} + 4 x ^{3} + 12 x ^{2} + 16 x + 16 )}

乘开

(x + 2) (x^{4} + 4 x^{3} + 12 x^{2} + 16 x + 16) : x^{5} + 6 x^{4} + 20 x^{3} + 40 x^{2} + 48 x + 32

= \frac{d x}{x ^{5} + 6 x ^{4} + 20 x ^{3} + 40 x ^{2} + 48 x + 32}

e x p an d - \frac{1}{( x - 5 ) ^{2}}

e x p an d - \frac{1.2 ( 1 - 0.03 x ^{2} )}{( 0.01 x ^{2} + 1 ) ^{3}}

\frac{d}{d t} ((W (t)) (t - W (t)) \cdot g (t))

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

e x p an d \frac{4 ( n + 1 ) ( 2 n + 1 )}{n ^{2}}