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

Lösung

erweitern

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

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

Schritte zur Lösung

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

Wende Ausklammerungsregel an (VANI):

(a + b) (c + d) = a c + a d + b c + b d

a = x^{2}, b = 1, c = ln (x^{2} + 1), d = - 1

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

Wende Minus-Plus Regeln an

+ (- a) = - a

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

Vereinfache

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

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

e x p an d l (e^{2} (t - 3) cos (t - 3))

e x p an d \frac{3}{( 3 x )}

e x p an d \frac{( b + x ) ^{4}}{4}

e x p an d (x + 1)^{5} e^{3 x^{2}}

e x p an d, (5 a^{2} - 2 b + c^{3}) (3 x - 2 y - 5 z + 2)