展开 (x^2+5)^32xdx

解答

展开

(x^{2} + 5)^{3} 2 x d x

2 x^{7} d x + 30 x^{5} d x + 150 x^{3} d x + 250 x d x

求解步骤

(x^{2} + 5)^{3} \cdot 2 x d x

(x^{2} + 5)^{3} = x^{6} + 15 x^{4} + 75 x^{2} + 125

= 2 x (x^{6} + 15 x^{4} + 75 x^{2} + 125) d x

= 2 x (x^{6} + 15 x^{4} + 75 x^{2} + 125) d x

打开括号

= 2 x d x x^{6} + 2 x d x \cdot 15 x^{4} + 2 x d x \cdot 75 x^{2} + 2 x d x \cdot 125

= 2 x^{6} x d x + 2 \cdot 15 x^{4} x d x + 2 \cdot 75 x^{2} x d x + 2 \cdot 125 x d x

化简

2 x^{6} x d x + 2 \cdot 15 x^{4} x d x + 2 \cdot 75 x^{2} x d x + 2 \cdot 125 x d x : 2 x^{7} d x + 30 x^{5} d x + 150 x^{3} d x + 250 x d x

= 2 x^{7} d x + 30 x^{5} d x + 150 x^{3} d x + 250 x d x

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

\frac{d}{d t} ((x) (x + 2 y))

e x p an d \frac{2 ( 2299 11 - 1029 21 )}{4375}

e x p an d \frac{( x - 1 ) ^{4} n ( x ^{3} + 8 ) ( x - 4 )}{( x ^{2} - 2 x + 2 )}

e x p an d (3 + 4 y^{2} + 4 y)^{5}