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

Lösung

erweitern

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

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

Schritte zur Lösung

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

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

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

Setze Klammern

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

Wende Minus-Plus Regeln an

+ (- a) = - a

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

Vereinfache

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

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

e x p an d (e^{x} + e^{6})^{2}

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

e x p an d 5 (x^{2} \cdot \frac{x}{5} \cdot \frac{3}{4})

e x p an d (3 e^{3 x + 1} + e)^{4}

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