erweitern (x(x^2+1)^3)dx

Lösung

erweitern

(x (x^{2} + 1)^{3}) d x

x^{7} d x + 3 x^{5} d x + 3 x^{3} d x + x d x

Schritte zur Lösung

(x (x^{2} + 1)^{3}) d x

Entferne die Klammern:

(a) = a

= x (x^{2} + 1)^{3} d x

(x^{2} + 1)^{3} = x^{6} + 3 x^{4} + 3 x^{2} + 1

= x (x^{6} + 3 x^{4} + 3 x^{2} + 1) d x

Setze Klammern

= x d x x^{6} + x d x \cdot 3 x^{4} + x d x \cdot 3 x^{2} + x d x \cdot 1

= x^{6} x d x + 3 x^{4} x d x + 3 x^{2} x d x + 1 \cdot x d x

Vereinfache

x^{6} x d x + 3 x^{4} x d x + 3 x^{2} x d x + 1 \cdot x d x : x^{7} d x + 3 x^{5} d x + 3 x^{3} d x + x d x

= x^{7} d x + 3 x^{5} d x + 3 x^{3} d x + x d x

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

e x p an d \frac{( x - 6 ) ^{2}}{( 2 - 3 x )}

e x p an d - 2 [x (x + 3) (x - 1) (x - 4)]

e x p an d (e^{x} - 1) e^{x}

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