本题目来源于试卷: Integral Calculus，类别为 IB数学
[问答题]
1. Using the substity4c/jd8kyt kkuj e4xp 48 -l+lutizm+tav3w*9pvhn5 g/mwk 9 t.von $x=\cot \theta$ , 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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