2

$$\int_{0}^{\frac{\pi}{2}}x^2\sqrt{\tan{x}}\sin{2x}dx=\frac{\pi\sqrt{2}}{32}\left[\frac{5\pi^2}{6}+2\pi-2\pi\log{2}-4+4\log{2}-2\log^2{2}\right] $$

I think this integral is very nice. and I think this integral have nice methods?

my methods:let $\sqrt{\tan{x}}=t$

math110
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    prove this integral... I can't, integrals are never proven (but some of them may be computed). – Did Mar 25 '13 at 16:29
  • What happened to my comment? I believe this is a duplicate of this question: http://math.stackexchange.com/questions/284933/a-hard-definite-integral-with-trignometric/284952#284952 – Ron Gordon Mar 25 '13 at 16:40
  • oh,Thank you,I can't found this question has been asked before.Thank you – math110 Mar 26 '13 at 02:11

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