erweitern (ysqrt(x^2+y^2))dx-x(x+sqrt(x^2+y^2))dy

Lösung

erweitern

(y x^{2} + y^{2}) d x - x (x + x^{2} + y^{2}) d y

y x^{2} + y^{2} d x - x^{2} d y - x d y x^{2} + y^{2}

Schritte zur Lösung

(y x^{2} + y^{2}) d x - x (x + x^{2} + y^{2}) d y

Multipliziere aus

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

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

Entferne die Klammern:

(a) = a

= y x^{2} + y^{2} d x - x^{2} d y - x d y x^{2} + y^{2}

e x p an d (1, 2, 3) x (- 2, - 2, 4)

e x p an d \frac{x ^{2} + 20 x + 31}{( x + 2 ) ^{2} ( x - 3 )}

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

e x p an d \frac{6 x ^{2} + 20 x + 3}{( 3 x + 5 ) ^{2}}

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