展开 (y^3+15xy^4-2x)dx+(3xy^2+20x^2y^3)dx

解答

展开

(y^{3} + 15 x y^{4} - 2 x) d x + (3 x y^{2} + 20 x^{2} y^{3}) d x

y^{3} d x + 15 y^{4} x d x - 2 x d x + 3 y^{2} x d x + 20 y^{3} x^{2} d x

求解步骤

(y^{3} + 15 x y^{4} - 2 x) d x + (3 x y^{2} + 20 x^{2} y^{3}) d x

= (y^{3} + 15 y^{4} x - 2 x) d x + (3 y^{2} x + 20 y^{3} x^{2}) d x

乘开

d x (y^{3} + 15 x y^{4} - 2 x) : y^{3} d x + 15 y^{4} x d x - 2 x d x

= y^{3} d x + 15 y^{4} x d x - 2 x d x + (3 x y^{2} + 20 x^{2} y^{3}) d x

乘开

d x (3 x y^{2} + 20 x^{2} y^{3}) : 3 y^{2} x d x + 20 y^{3} x^{2} d x

= y^{3} d x + 15 y^{4} x d x - 2 x d x + 3 y^{2} x d x + 20 y^{3} x^{2} d x

e x p an d \frac{3}{s ( s + 1 ) ^{2}}

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

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

e x p an d \frac{a}{12} \cdot \frac{9}{10}

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