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人気のある微分積分 >

integral from ln(2) to ln(10) of tanh(x)

解

\int_{l n (2)}^{l n (10)} tanh (x) d x

解

ln (\frac{101}{25})

+1

十進法表記

1.39624 \dots

解答ステップ

\int_{l n (2)}^{l n (10)} tanh (x) d x

三角関数の公式を使用して書き換える

= \int_{l n (2)}^{l n (10)} \frac{sinh ( x )}{cosh ( x )} d x

u置換積分法を適用する

= \int_{\frac{5}{4}}^{\frac{101}{20}} \frac{1}{u} d u

共通積分を使用する:

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{\frac{5}{4}}^{\frac{101}{20}}

限度を計算する:

ln (\frac{101}{20}) - ln (\frac{5}{4})

= ln (\frac{101}{20}) - ln (\frac{5}{4})

簡素化

= ln (\frac{101}{25})

グラフ

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