erweitern x^2y^2(2+y/x)dx+x^2y^2(x/y+2)dy

Lösung

erweitern

x^{2} y^{2} (2 + \frac{y}{x}) d x + x^{2} y^{2} (\frac{x}{y} + 2) d y

2 x^{2} y^{2} d x + x y^{3} d x + x^{3} y d y + 2 x^{2} y^{2} d y

Schritte zur Lösung

x^{2} y^{2} (2 + \frac{y}{x}) d x + x^{2} y^{2} (\frac{x}{y} + 2) d y

Multipliziere aus

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

= 2 x^{2} y^{2} d x + x y^{3} d x + x^{2} y^{2} (\frac{x}{y} + 2) d y

Multipliziere aus

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

= 2 x^{2} y^{2} d x + x y^{3} d x + x^{3} y d y + 2 x^{2} y^{2} d y

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

e x p an d (1 - sin (x)) (sec (x) - tan (x))

e x p an d \frac{12}{( x + 2 ) ^{2}}

e x p an d \frac{e ^{- s}}{s ( s + 6 )}

s im pl i f y (3 - x) (9 - x^{2})