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

Lösung

erweitern

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

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

Schritte zur Lösung

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

Wende Ausklammerungsregel an (VANI):

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

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

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

Vereinfache

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

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

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

s im pl i f y (4 1 + x^{4} + x) (4 1 + x^{4} - x)

e x p an d 1 + \frac{x ^{6}}{4} - \frac{1}{2} + \frac{1}{4 x ^{6}}

e x p an d lo g_{10} (3 8 + 7 x)

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