簡約 1/7 ln|9.3+1|-1/7 ln|9.3+8|+C

解

簡約

\frac{1}{7} ln ∣ 9.3 + 1 ∣ - \frac{1}{7} ln ∣ 9.3 + 8 ∣ + C

ln (0.92859 \dots) + C

解答ステップ

\frac{1}{7} ln ∣ 9.3 + 1 ∣ - \frac{1}{7} ln ∣ 9.3 + 8 ∣ + C

対数の規則を適用する:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{1}{7} ln ∣ 1 + 9.3 ∣ = ln (∣ 1 + 9.3 ∣^{\frac{1}{7}})

= ln (∣ 1 + 9.3 ∣^{\frac{1}{7}}) - \frac{1}{7} ln ∣ 8 + 9.3 ∣ + C

対数の規則を適用する:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{1}{7} ln ∣ 8 + 9.3 ∣ = ln (∣ 8 + 9.3 ∣^{\frac{1}{7}})

= ln (∣ 1 + 9.3 ∣^{\frac{1}{7}}) - ln (∣ 8 + 9.3 ∣^{\frac{1}{7}}) + 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 (∣ 9.3 + 1 ∣^{\frac{1}{7}}) - ln (∣ 9.3 + 8 ∣^{\frac{1}{7}}) = ln (\frac{∣ 1 + 9.3 ∣ ^{\frac{1}{7}}}{∣ 8 + 9.3 ∣ ^{\frac{1}{7}}})

= ln (\frac{∣ 1 + 9.3 ∣ ^{\frac{1}{7}}}{∣ 8 + 9.3 ∣ ^{\frac{1}{7}}}) + C

\frac{∣ 9.3 + 1 ∣ ^{\frac{1}{7}}}{∣ 9.3 + 8 ∣ ^{\frac{1}{7}}} = 0.92859 \dots

= ln (0.92859 \dots) + C