［Ｑ］∫(0,φ)ｄθ／ｃｏｓθ＝？

を変数変換しないで求めてみる．

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１／ｃｏｓθ＝１／ｓｉｎ(θ＋π/2)＝１／２ｓｉｎ(θ/2＋π/4)ｃｏｓ(θ/2＋π/4)

＝１／２・｛ｃｏｓ(θ/2＋π/4)／ｓｉｎ(θ/2＋π/4)＋ｓｉｎ(θ/2＋π/4)／ｃｏｓ(θ/2＋π/4)

∫ｄθ／ｃｏｓθ

＝ｌｏｇｓｉｎ(θ/2＋π/4)−ｌｏｇｃｏｓ(θ/2＋π/4)

＝ｌｏｇｔａｎ(θ/2＋π/4)

∫(0,φ)ｄθ／ｃｏｓθ＝ｌｏｇｔａｎ(φ/2＋π/4)

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