展开 (y^2e^{xy^2}+4x^3)dx+(2xye^{xy^2}-3y^2)dy

解答

展开

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

e^{y^{2} x} y^{2} d x + 4 x^{3} d x + 2 e^{y^{2} x} y x d y - 3 y^{2} d y

求解步骤

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

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

乘开

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

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

乘开

d y (2 x y e^{x y^{2}} - 3 y^{2}) : 2 e^{y^{2} x} y x d y - 3 y^{2} d y

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

e x p an d \frac{x ^{4} + 4 x ^{2} - 9}{4 x ( x ^{2} + 6 x - 9 )}

e x p an d \frac{( 4 x ^{2} + 5 )}{( x ^{2} + 1 ) ( x ^{2} + 9 )}

e x p an d \frac{3}{x ^{2} - 2 x + 1} + \frac{2}{x ^{2} - 1}

e x p an d sin (e^{x} + x) (1 + cos (x))^{14}

e x p an d cos ((2 n - 1) π)