erweitern (ycos(xy)-3x^2)dx+(xcos(xy)+3y^2)dy

Lösung

erweitern

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

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

Schritte zur Lösung

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

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

Multipliziere aus

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

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

Multipliziere aus

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

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

e x p an d \frac{2}{9} x^{3} y^{2} - \frac{4}{3} x y^{3}

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

e x p an d \frac{81 ( 1 3 ^{15} - 1 )}{1 3 ^{15} \cdot 2}

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

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