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積分問題30番
思考
部分分数分解します。
計算
\(\displaystyle\int\displaystyle\frac{dx}{(x-1)^2(x^2+1)}\)
\(=\displaystyle\int\displaystyle\frac{x}{2(x^2+1)}dx-\displaystyle\int\displaystyle\frac{dx}{2(x-1)}+\displaystyle\int\displaystyle\frac{dx}{2(x-1)^2}\) （部分分数分解）
\(=\displaystyle\frac{1}{4}\log(x^2+1)-\displaystyle\frac{1}{2}\log|x-1|-\displaystyle\frac{1}{2x-2}+C\)
答え
\(\displaystyle\frac{1}{4}\log(x^2+1)-\displaystyle\frac{1}{2}\log|x-1|-\displaystyle\frac{1}{2x-2}+C\)
