erweitern (y^3+5xy^4-2x)dx+(3xy^2+20x^2y^3)dx

Lösung

erweitern

(y^{3} + 5 x y^{4} - 2 x) d x + (3 x y^{2} + 20 x^{2} y^{3}) d x

y^{3} d x + 5 y^{4} x d x - 2 x d x + 3 y^{2} x d x + 20 y^{3} x^{2} d x

Schritte zur Lösung

(y^{3} + 5 x y^{4} - 2 x) d x + (3 x y^{2} + 20 x^{2} y^{3}) d x

= (y^{3} + 5 y^{4} x - 2 x) d x + (3 y^{2} x + 20 y^{3} x^{2}) d x

Multipliziere aus

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

= y^{3} d x + 5 y^{4} x d x - 2 x d x + (3 x y^{2} + 20 x^{2} y^{3}) d x

Multipliziere aus

d x (3 x y^{2} + 20 x^{2} y^{3}) : 3 y^{2} x d x + 20 y^{3} x^{2} d x

= y^{3} d x + 5 y^{4} x d x - 2 x d x + 3 y^{2} x d x + 20 y^{3} x^{2} d x

e x p an d (y^{3} + 5 x y^{4} - 2 x) d x + (3 x y^{2} + 20 x^{2} y^{3}) d y

e x p an d (x) d x + (y - 2 x) d y

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

e x p an d \frac{Δ x ( - x + 1 )}{( x + Δ x + 1 ) ( x + 1 )}

e x p an d (x^{2} - 6 x - 8) cos (x - 2)