erweitern 1/5 (3ln|(x^2)/4+1|+2arctan(x/2))

Lösung

erweitern

\frac{1}{5} (3 ln \frac{x ^{2}}{4} + 1 + 2 arctan (\frac{x}{2}))

\frac{3}{5} ln \frac{x ^{2}}{4} + 1 + \frac{2}{5} arctan (\frac{x}{2})

Schritte zur Lösung

\frac{1}{5} (3 ln \frac{x ^{2}}{4} + 1 + 2 arctan (\frac{x}{2}))

Wende das Distributivgesetz an:

a (b + c) = ab + a c

a = \frac{1}{5}, b = 3 ln \frac{x ^{2}}{4} + 1, c = 2 arctan (\frac{x}{2})

= \frac{1}{5} \cdot 3 ln \frac{x ^{2}}{4} + 1 + \frac{1}{5} \cdot 2 arctan (\frac{x}{2})

= 3 \cdot \frac{1}{5} ln \frac{x ^{2}}{4} + 1 + 2 \cdot \frac{1}{5} arctan (\frac{x}{2})

Vereinfache

3 \cdot \frac{1}{5} ln \frac{x ^{2}}{4} + 1 + 2 \cdot \frac{1}{5} arctan (\frac{x}{2}) : \frac{3}{5} ln \frac{x ^{2}}{4} + 1 + \frac{2}{5} arctan (\frac{x}{2})

= \frac{3}{5} ln \frac{x ^{2}}{4} + 1 + \frac{2}{5} arctan (\frac{x}{2})

e x p an d \frac{3 x ^{3} + 2 x - 1}{x ( x + 1 ) ( x - 7 )}

e x p an d (- sin (t) + cos (t)) \cdot (- cos (t) - sin (t))

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

e x p an d (e^{- 3 (x - y)} + cos (x - y)) (e^{- 3 x} + e^{2 x})

e x p an d 1 + \frac{81}{20} (3 x - 2)