実行日時: 2026-08-10T11:54:55（ID: 20260810-115455-ac715e） ← 履歴一覧に戻る
問題TeXソース
¥begin{enumerate}
¥item 次の積分を求めよ。
¥begin{edaenumerate}
¥item $¥displaystyle ¥int_{0}^{¥frac{¥pi}{4}} ¥cos^2 x dx$ ¥vspace{15ZW}
¥item $¥displaystyle ¥int_{0}^{¥frac{¥pi}{4}} ¥cos^3 x dx$ ¥vspace{15ZW}
¥item $¥displaystyle ¥int_{0}^{¥frac{¥pi}{4}} ¥cos^4 x dx$ ¥vspace{15ZW}
¥item $¥displaystyle ¥int_{0}^{¥frac{¥pi}{4}} ¥cos^5 x dx$ ¥vspace{15ZW}
¥item $¥displaystyle ¥int_{0}^{¥frac{¥pi}{4}} ¥dfrac{1}{¥cos x} dx$ ¥vspace{15ZW}
¥item $¥displaystyle ¥int_{0}^{¥frac{¥pi}{4}} ¥dfrac{1}{¥cos^2 x} dx$ ¥vspace{15ZW}
¥item $¥displaystyle ¥int_{0}^{¥frac{¥pi}{4}} ¥dfrac{1}{¥cos^3 x} dx$ ¥vspace{15ZW}
¥item $¥displaystyle ¥int_{0}^{¥frac{¥pi}{4}} ¥dfrac{1}{¥cos^4 x} dx$ ¥vspace{15ZW}
¥newpage
¥item $¥displaystyle ¥int_{1}^{2} x e^x dx$ ¥vspace{15ZW}
¥item $¥displaystyle ¥int_{1}^{2} x^2 e^x dx$ ¥vspace{15ZW}
¥item $¥displaystyle ¥int_{1}^{2} x e^{x^2} dx$ ¥vspace{15ZW}
¥item $¥displaystyle ¥int_{1}^{2} x^3 e^{x^2} dx$ ¥vspace{15ZW}
¥item $¥displaystyle ¥int_{1}^{2} e^{¥sqrt{x}} dx$ ¥vspace{15ZW}
¥item $¥displaystyle ¥int_{1}^{2} e^{¥sqrt[3]{x}} dx$ ¥vspace{15ZW}
¥item $¥displaystyle ¥int_{1}^{e} ¥log x dx$ ¥vspace{15ZW}
¥item $¥displaystyle ¥int_{1}^{e} x ¥log x dx$ ¥vspace{15ZW}
¥item $¥displaystyle ¥int_{1}^{e} x^2 ¥log x dx$ ¥vspace{15ZW}
¥item $¥displaystyle ¥int_{1}^{e} x (¥log x)^2 dx$ ¥vspace{15ZW}
¥item $¥displaystyle ¥int_{1}^{e} x (¥log x)^3 dx$ ¥vspace{15ZW}
¥item $¥displaystyle ¥int_{1}^{e} ¥dfrac{¥log x}{x} dx$ ¥vspace{15ZW}
¥item $¥displaystyle ¥int_{1}^{e} ¥dfrac{(¥log x)^2}{x} dx$ ¥vspace{15ZW}
¥item $¥displaystyle ¥int_{1}^{e} ¥dfrac{¥log x}{x^2} dx$ ¥vspace{15ZW}
¥item $¥displaystyle ¥int_{0}^{1} ¥sqrt{4-x} dx$ ¥vspace{15ZW}
¥item $¥displaystyle ¥int_{0}^{1} ¥dfrac{1}{¥sqrt{4-x}} dx$ ¥vspace{15ZW}
¥item $¥displaystyle ¥int_{0}^{1} ¥sqrt{4-x^2} dx$ ¥vspace{15ZW}
¥item $¥displaystyle ¥int_{0}^{1} ¥dfrac{1}{¥sqrt{4-x^2}} dx$ ¥vspace{15ZW}
¥item $¥displaystyle ¥int_{0}^{1} x¥sqrt{4-x} dx$ ¥vspace{15ZW}
¥item $¥displaystyle ¥int_{0}^{1} ¥dfrac{x}{¥sqrt{4-x}} dx$ ¥vspace{15ZW}
¥item $¥displaystyle ¥int_{0}^{1} x¥sqrt{4-x^2} dx$ ¥vspace{15ZW}
¥item $¥displaystyle ¥int_{0}^{1} x^2¥sqrt{4-x^2} dx$ ¥vspace{15ZW}
¥item $¥displaystyle ¥int_{0}^{1} ¥dfrac{1}{x^2+1} dx$ ¥vspace{15ZW}
¥item $¥displaystyle ¥int_{0}^{1} ¥dfrac{x}{x^2+1} dx$ ¥vspace{15ZW}
¥item $¥displaystyle ¥int_{0}^{1} ¥dfrac{x^2}{x^2+1} dx$ ¥vspace{15ZW}
¥item $¥displaystyle ¥int_{0}^{1} ¥dfrac{1}{(x^2+1)^2} dx$ ¥vspace{15ZW}
¥item $¥displaystyle ¥int_{0}^{1} ¥dfrac{1}{¥sqrt{x^2+1}} dx$ ¥vspace{15ZW}
¥item $¥displaystyle ¥int_{0}^{1} ¥dfrac{x}{¥sqrt{x^2+1}} dx$ ¥vspace{15ZW}
¥item $¥displaystyle ¥int_{0}^{1} ¥sqrt{x^2+1} dx$ ¥vspace{15ZW}
¥item $¥displaystyle ¥int_{0}^{1} ¥dfrac{x^2}{¥sqrt{x^2+1}} dx$ ¥vspace{15ZW}
¥end{edaenumerate}
¥end{enumerate}
GPT生成 解答TeX（検査前）
\begin{enumerate}
\item
\begin{edaenumerate}
\item $\dfrac{\pi}{8}+\dfrac{1}{4}$
\item $\dfrac{5\sqrt{2}}{12}$
\item $\dfrac{3\pi}{32}+\dfrac{1}{4}$
\item $\dfrac{43\sqrt{2}}{120}$
\item $\log(1+\sqrt{2})$
\item $1$
\item $\dfrac{\sqrt{2}+\log(1+\sqrt{2})}{2}$
\item $\dfrac{4}{3}$
\item $e^2$
\item $2e^2-e$
\item $\dfrac{e^4-e}{2}$
\item $\dfrac{3e^4}{2}$
\item $2(\sqrt{2}-1)e^{\sqrt{2}}$
\item $3e^{\sqrt[3]{2}}\left(\sqrt[3]{4}-2\sqrt[3]{2}+2\right)-3e$
\item $1$
\item $\dfrac{e^2+1}{4}$
\item $\dfrac{2e^3+1}{9}$
\item $\dfrac{e^2-1}{4}$
\item $\dfrac{e^2+3}{8}$
\item $\dfrac{1}{2}$
\item $\dfrac{1}{3}$
\item $1-\dfrac{2}{e}$
\item $\dfrac{16}{3}-2\sqrt{3}$
\item $4-2\sqrt{3}$
\item $\dfrac{\sqrt{3}}{2}+\dfrac{\pi}{3}$
\item $\dfrac{\pi}{6}$
\item $\dfrac{128-66\sqrt{3}}{15}$
\item $\dfrac{32}{3}-6\sqrt{3}$
\item $\dfrac{8}{3}-\sqrt{3}$
\item $\dfrac{\pi}{3}-\dfrac{\sqrt{3}}{4}$
\item $\dfrac{\pi}{4}$
\item $\dfrac{\log 2}{2}$
\item $1-\dfrac{\pi}{4}$
\item $\dfrac{1}{4}+\dfrac{\pi}{8}$
\item $\log(1+\sqrt{2})$
\item $\sqrt{2}-1$
\item $\dfrac{\sqrt{2}+\log(1+\sqrt{2})}{2}$
\item $\dfrac{\sqrt{2}-\log(1+\sqrt{2})}{2}$
\end{edaenumerate}
\end{enumerate}
Claudeによる指摘事項
誤りなし
修正後の解答TeX（最終）
\begin{enumerate}
\item
\begin{edaenumerate}
\item $\dfrac{\pi}{8}+\dfrac{1}{4}$
\item $\dfrac{5\sqrt{2}}{12}$
\item $\dfrac{3\pi}{32}+\dfrac{1}{4}$
\item $\dfrac{43\sqrt{2}}{120}$
\item $\log(1+\sqrt{2})$
\item $1$
\item $\dfrac{\sqrt{2}+\log(1+\sqrt{2})}{2}$
\item $\dfrac{4}{3}$
\item $e^2$
\item $2e^2-e$
\item $\dfrac{e^4-e}{2}$
\item $\dfrac{3e^4}{2}$
\item $2(\sqrt{2}-1)e^{\sqrt{2}}$
\item $3e^{\sqrt[3]{2}}\left(\sqrt[3]{4}-2\sqrt[3]{2}+2\right)-3e$
\item $1$
\item $\dfrac{e^2+1}{4}$
\item $\dfrac{2e^3+1}{9}$
\item $\dfrac{e^2-1}{4}$
\item $\dfrac{e^2+3}{8}$
\item $\dfrac{1}{2}$
\item $\dfrac{1}{3}$
\item $1-\dfrac{2}{e}$
\item $\dfrac{16}{3}-2\sqrt{3}$
\item $4-2\sqrt{3}$
\item $\dfrac{\sqrt{3}}{2}+\dfrac{\pi}{3}$
\item $\dfrac{\pi}{6}$
\item $\dfrac{128-66\sqrt{3}}{15}$
\item $\dfrac{32}{3}-6\sqrt{3}$
\item $\dfrac{8}{3}-\sqrt{3}$
\item $\dfrac{\pi}{3}-\dfrac{\sqrt{3}}{4}$
\item $\dfrac{\pi}{4}$
\item $\dfrac{\log 2}{2}$
\item $1-\dfrac{\pi}{4}$
\item $\dfrac{1}{4}+\dfrac{\pi}{8}$
\item $\log(1+\sqrt{2})$
\item $\sqrt{2}-1$
\item $\dfrac{\sqrt{2}+\log(1+\sqrt{2})}{2}$
\item $\dfrac{\sqrt{2}-\log(1+\sqrt{2})}{2}$
\end{edaenumerate}
\end{enumerate}