erweitern (x+ln^2(x))^3

Lösung

erweitern

(x + ln^{2} (x))^{3}

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

Schritte zur Lösung

(x + ln^{2} (x))^{3}

Wende Formel für perfekte dritte Potenzen an:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

a = x, b = ln^{2} (x)

= x^{3} + 3 x^{2} ln^{2} (x) + 3 x (ln^{2} (x))^{2} + (ln^{2} (x))^{3}

Vereinfache

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

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

e x p an d 4 x y^{2} - 2 x y + \frac{( 4 x ^{2} y - x ^{2} - 5 ) d y}{d x}

f a c t or x^{4} (δ (x - 2)) d x

e x p an d 3 \cdot (7 \cdot 4 y)

e x p an d \frac{- i ( 1 + i ) ^{n} - 1 + i + ( 1 + i ) ^{n}}{( 1 + i ) ^{n}}

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