展开 (3x^2+y^2)dx-(ax^2+2bxy)dy

解答

展开

(3 x^{2} + y^{2}) d x - (a x^{2} + 2 b x y) d y

3 x^{2} d x + y^{2} d x - a x^{2} d y - 2 b x y d y

求解步骤

(3 x^{2} + y^{2}) d x - (a x^{2} + 2 b x y) d y

乘开

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

= 3 x^{2} d x + y^{2} d x - (a x^{2} + 2 b x y) d y

乘开

- d y (a x^{2} + 2 b x y) : - a x^{2} d y - 2 b x y d y

= 3 x^{2} d x + y^{2} d x - a x^{2} d y - 2 b x y d y

e x p an d x^{2} (e^{3 s} - 1)

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

e x p an d \frac{12 x + 7}{4} - \frac{30 - 18 x}{6}

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

e x p an d \frac{e ^{t} ( cos ( t ) - cos ( 2 t ) )}{t}