erweitern ln(1+x)(2(1+x)^2)

Lösung

erweitern

ln (1 + x) (2 (1 + x)^{2})

2 ln (1 + x) + 4 x ln (1 + x) + 2 x^{2} ln (1 + x)

Schritte zur Lösung

ln (1 + x) (2 (1 + x)^{2})

Entferne die Klammern:

(a) = a

= ln (1 + x) \cdot 2 (1 + x)^{2}

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

= 2 ln (x + 1) (x^{2} + 2 x + 1)

= 2 ln (1 + x) (1 + 2 x + x^{2})

Setze Klammern

= ln (1 + x) \cdot 2 \cdot 1 + ln (1 + x) \cdot 2 \cdot 2 x + ln (1 + x) \cdot 2 x^{2}

= 2 \cdot 1 \cdot ln (1 + x) + 2 \cdot 2 x ln (1 + x) + 2 x^{2} ln (1 + x)

Vereinfache

2 \cdot 1 \cdot ln (1 + x) + 2 \cdot 2 x ln (1 + x) + 2 x^{2} ln (1 + x) : 2 ln (1 + x) + 4 x ln (1 + x) + 2 x^{2} ln (1 + x)

= 2 ln (1 + x) + 4 x ln (1 + x) + 2 x^{2} ln (1 + x)

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

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

e x p an d \frac{2 x - 1}{( x + 2 ) ( x ^{2} + 3 )}

e x p an d \frac{1}{2} ((8, - 1) - (- 2, 5))

e x p an d y^{2} d t + (2 y t + 1) d y