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

Lösung

erweitern

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

3 x^{10} d x - 24 x^{8} d x + 72 x^{6} d x - 96 x^{4} d x + 48 x^{2} d x

Schritte zur Lösung

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

(x^{2} - 2)^{4} = x^{8} - 8 x^{6} + 24 x^{4} - 32 x^{2} + 16

= 3 x^{2} (x^{8} - 8 x^{6} + 24 x^{4} - 32 x^{2} + 16) d x

Setze Klammern

= 3 x^{2} d x x^{8} + 3 x^{2} d x (- 8 x^{6}) + 3 x^{2} d x \cdot 24 x^{4} + 3 x^{2} d x (- 32 x^{2}) + 3 x^{2} d x \cdot 16

Wende Minus-Plus Regeln an

+ (- a) = - a

= 3 x^{8} x^{2} d x - 3 \cdot 8 x^{6} x^{2} d x + 3 \cdot 24 x^{4} x^{2} d x - 3 \cdot 32 x^{2} x^{2} d x + 3 \cdot 16 x^{2} d x

Vereinfache

3 x^{8} x^{2} d x - 3 \cdot 8 x^{6} x^{2} d x + 3 \cdot 24 x^{4} x^{2} d x - 3 \cdot 32 x^{2} x^{2} d x + 3 \cdot 16 x^{2} d x : 3 x^{10} d x - 24 x^{8} d x + 72 x^{6} d x - 96 x^{4} d x + 48 x^{2} d x

= 3 x^{10} d x - 24 x^{8} d x + 72 x^{6} d x - 96 x^{4} d x + 48 x^{2} d x

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

e x p an d (tan (x) + sec (x)) \cdot cos (x)

e x p an d (x + d e lt a x)^{2}

e x p an d - 3 l e f t (x + 1)^{2} + 12

e x p an d (x + d e lt a x)^{3}