本题目来源于试卷: Integral Calculus，类别为 IB数学
[问答题]
1. Using the substitu hrt1 x1atkc5 3,elz;iti oxepw6om/zq+jyg qq-wk/ 3y +:;wn.aon $x=\cot \theta$ , show that $\int_{0}^{1} \frac{1}{\left(x^{2}+1\right)^{2}} \mathrm{~d} x=\int_{\frac{\pi}{4}}^{\frac{\pi}{2}} \sin ^{2} \theta \mathrm{d} \theta$ .
2. Hence find the value of $\int_{0}^{1} \frac{1}{\left(x^{2}+1\right)^{2}} \mathrm{~d} x$ .
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