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\(\int_0^{+\infty} \frac{ d t}{(1+t^2)^2} = \frac{\pi}{4}\)
\(\int_{-\infty}^{+\infty} \frac{ d t}{t^2+2t+2} = \pi\)
\(\int_0^{+\infty} \frac{ d t}{(1+t^2)^4} = \frac{ 5\pi}{32}\)
\(\int_{-\infty}^{+\infty} \frac{ d t}{(t^2+1)(t^2-2t\cos\alpha+1)} = \frac{\pi}{2|\sin\alpha|}\)
\(\int_0^{+\infty} \frac{ 2t^2+1}{(t^2+1)^2} \,d t = \frac{ 3\pi}{4}\)
\(\int_{-\infty}^{+\infty} \frac{ t^2\,d t}{(t^2+1)(t^2+a^2)} = \frac{ \pi}{1+|a|}\)
\(\int_0^{+\infty} \frac{ d t}{1+t^4} = \frac{\pi}{2\sqrt2}\)
\(\int_0^{+\infty} \frac{ t^2\,d t}{1+t^4} = \frac{\pi}{2\sqrt2}\)
\(\int_1^{+\infty} \frac{ d t}{t^6(1+t^{10})} = \frac{ 4-\pi}{20}\)