展開する 1/5 (3ln|(x^2)/4+1|+2arctan(x/2))

解

展開する

\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})

解答ステップ

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

分配法則を適用する:

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})

簡素化

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})