I've just found the following example on Piskunov:(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\int \frac{t^2 dt}{(t^2 + 2)^2}\\= \frac{1}{2}\int \frac{t d(t^2 +2)}{(t^2 + 2)^2}\\=-\frac{1}{2}\int t d(\frac{1}{t^2 + 2})\\=-\frac{1}{2}\frac{t}{t^2 + 2}+\int \frac{dt}{t^2 + 2}\\=-\frac{t}{2(t^2 + 2)} + \frac{1}{2 \sqrt{2}}arctan\frac{t}{\sqrt{2}}[/itex]

What technique is this? Apparently there is a substitution at the beginning, but I can't figure out what happens from second line onwards.

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# Which integration technique was used here?

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