erweitern x^2(3x^3-2)^4dx

Lösung

erweitern

x^{2} (3 x^{3} - 2)^{4} d x

81 x^{14} d x - 216 x^{11} d x + 216 x^{8} d x - 96 x^{5} d x + 16 x^{2} d x

Schritte zur Lösung

x^{2} (3 x^{3} - 2)^{4} d x

(3 x^{3} - 2)^{4} = 81 x^{12} - 216 x^{9} + 216 x^{6} - 96 x^{3} + 16

= x^{2} (81 x^{12} - 216 x^{9} + 216 x^{6} - 96 x^{3} + 16) d x

Setze Klammern

= x^{2} d x \cdot 81 x^{12} + x^{2} d x (- 216 x^{9}) + x^{2} d x \cdot 216 x^{6} + x^{2} d x (- 96 x^{3}) + x^{2} d x \cdot 16

Wende Minus-Plus Regeln an

+ (- a) = - a

= 81 x^{12} x^{2} d x - 216 x^{9} x^{2} d x + 216 x^{6} x^{2} d x - 96 x^{3} x^{2} d x + 16 x^{2} d x

Vereinfache

81 x^{12} x^{2} d x - 216 x^{9} x^{2} d x + 216 x^{6} x^{2} d x - 96 x^{3} x^{2} d x + 16 x^{2} d x : 81 x^{14} d x - 216 x^{11} d x + 216 x^{8} d x - 96 x^{5} d x + 16 x^{2} d x

= 81 x^{14} d x - 216 x^{11} d x + 216 x^{8} d x - 96 x^{5} d x + 16 x^{2} d x

e x p an d \frac{4}{( x + 1 ) ( x + 5 ) ( s - 3 )}

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

e x p an d \frac{( x - 2 ) ( - 3 x + 180 )}{x}

e x p an d \frac{( s + 1 )}{( s + 2 ) \cdot ( s + 4 )}

e x p an d \frac{s + 5}{( s + 4 ) ( s + 1 )}