erweitern (y^3x^2+2y)dx+x^2y^3(4ydx+5xdy)

Lösung

erweitern

(y^{3} x^{2} + 2 y) d x + x^{2} y^{3} (4 y d x + 5 x d y)

y^{3} x^{2} d x + 2 y d x + 4 y^{4} x^{2} d x + 5 y^{3} x^{3} d y

Schritte zur Lösung

(y^{3} x^{2} + 2 y) d x + x^{2} y^{3} (4 y d x + 5 x d y)

= (y^{3} x^{2} + 2 y) d x + y^{3} x^{2} (4 y d x + 5 x d y)

Multipliziere aus

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

= y^{3} x^{2} d x + 2 y d x + x^{2} y^{3} (4 y d x + 5 x d y)

Multipliziere aus

x^{2} y^{3} (4 y d x + 5 x d y) : 4 y^{4} x^{2} d x + 5 y^{3} x^{3} d y

= y^{3} x^{2} d x + 2 y d x + 4 y^{4} x^{2} d x + 5 y^{3} x^{3} d y

e x p an d 3 in (e^{x} + 1)

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

e x p an d (x - 5) (x - 5) (x - 2 i) (x + 2 i)

e x p an d \frac{14 x - 7 h}{x ^{2} ( x + h ) ^{2}}

e x p an d (\frac{1 + 5}{2})^{3}