erweitern f(x)(ln(x)-x^2)^3

Lösung

erweitern

f (x) (ln (x) - x^{2})^{3}

f x ln^{3} (x) - 3 f x^{3} ln^{2} (x) + 3 f x^{5} ln (x) - f x^{7}

Schritte zur Lösung

f (x) (ln (x) - x^{2})^{3}

Entferne die Klammern:

(a) = a

= f x (ln (x) - x^{2})^{3}

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

= f x (- x^{6} + 3 x^{4} ln (x) - 3 x^{2} ln^{2} (x) + ln^{3} (x))

Setze Klammern

= f x ln^{3} (x) + f x (- 3 x^{2} ln^{2} (x)) + f x \cdot 3 x^{4} ln (x) + f x (- x^{6})

Wende Minus-Plus Regeln an

+ (- a) = - a

= f x ln^{3} (x) - 3 f x^{2} x ln^{2} (x) + 3 f x^{4} x ln (x) - f x^{6} x

Vereinfache

f x ln^{3} (x) - 3 f x^{2} x ln^{2} (x) + 3 f x^{4} x ln (x) - f x^{6} x : f x ln^{3} (x) - 3 f x^{3} ln^{2} (x) + 3 f x^{5} ln (x) - f x^{7}

= f x ln^{3} (x) - 3 f x^{3} ln^{2} (x) + 3 f x^{5} ln (x) - f x^{7}

s im pl i f y (\frac{1}{x} \circ 7 - x) (x)

e x p an d \frac{5}{( x + 1 ) ^{2}}

e x p an d - 2 cos (2 (x - \frac{π}{4})) - 3

e x p an d r^{5^{^{'}}} (3 r^{5} + 4)

e x p an d 50 (47 - 6 ln (50))