erweitern 2.5x^{2.5sqrt(x)-0.5}(0.5ln(x)+1)

Lösung

erweitern

2.5 x^{2.5 x - 0.5} (0.5 ln (x) + 1)

1.25 x^{2.5 x - 0.5} ln (x) + 2.5 x^{2.5 x - 0.5}

Schritte zur Lösung

2.5 x^{2.5 x - 0.5} (0.5 ln (x) + 1)

Wende das Distributivgesetz an:

a (b + c) = ab + a c

a = 2.5 x^{2.5 x - 0.5}, b = 0.5 ln (x), c = 1

= 2.5 x^{2.5 x - 0.5} \cdot 0.5 ln (x) + 2.5 x^{2.5 x - 0.5} \cdot 1

= 0.5 \cdot 2.5 x^{2.5 x - 0.5} ln (x) + 1 \cdot 2.5 x^{2.5 x - 0.5}

Vereinfache

0.5 \cdot 2.5 x^{2.5 x - 0.5} ln (x) + 1 \cdot 2.5 x^{2.5 x - 0.5} : 1.25 x^{2.5 x - 0.5} ln (x) + 2.5 x^{2.5 x - 0.5}

= 1.25 x^{2.5 x - 0.5} ln (x) + 2.5 x^{2.5 x - 0.5}

e x p an d e^{x - 1} (1 + e^{1 - x})

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

s im pl i f y 2 (x - \frac{3}{2})

e x p an d \frac{1}{( z + j ) ( z - j )}

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