簡約-1/8 (ln|a+5/2 |-ln|a+1/2 |)+C

解

簡約

- \frac{1}{8} (ln a + \frac{5}{2} - ln a + \frac{1}{2}) + C

- \frac{1}{8} ln (\frac{∣ 2 a + 5 ∣}{∣ 2 a + 1 ∣}) + C

解答ステップ

- \frac{1}{8} (ln a + \frac{5}{2} - ln a + \frac{1}{2}) + C

対数の規則を適用する:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln a + \frac{5}{2} - ln a + \frac{1}{2} = ln (\frac{a + \frac{5}{2}}{a + \frac{1}{2}})

= - \frac{1}{8} ln (\frac{a + \frac{5}{2}}{a + \frac{1}{2}}) + C

簡素化

\frac{a + \frac{5}{2}}{a + \frac{1}{2}} : \frac{∣ 2 a + 5 ∣}{∣ 2 a + 1 ∣}

= - \frac{1}{8} ln (\frac{∣ 2 a + 5 ∣}{∣ 2 a + 1 ∣}) + C