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This year I am going to participate in an olympiad of indefinite integrals. The level is very high, I would like to know some (hard, olympiad) Indefinite integrals challenge problems

Note: Here is the olympiad 2013 Indefinite integrals 2013, this is what " high level" I refer to.

user316212
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  • Do you know http://integralsandseries.prophpbb.com/ ? – Watson Feb 20 '16 at 15:28
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    What is your definition of "quite high"? – Imago Feb 20 '16 at 15:30
  • @Imago That is not the point, the idea is a big list in challenge problems in indefinite integrlas. With 'high' I refer to non-elementary integrals. – user316212 Feb 20 '16 at 15:36
  • @Watson thanks! – user316212 Feb 20 '16 at 15:37
  • If you want to see some amazing integration look at some of this woman's answers: http://math.stackexchange.com/users/97378/cleo. – bubba Feb 20 '16 at 15:38
  • Related : http://math.stackexchange.com/questions/233162/list-of-interesting-integrals-for-early-calculus-students?rq=1 – Watson Feb 20 '16 at 15:40
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    I wanted to give a constructive answer, however it was very hard for me, to guess what very high level integrals actually means. Your question didn't seem very specific. The range of integrals between the level of trivial and unsolvable is quite broad. However I think Watson's source should be quite fulfilling. – Imago Feb 20 '16 at 15:45
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    The integral of $e^{\pi}$ is surely tough!!! So hard! – Enrico M. Feb 20 '16 at 19:19

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Try solving,

$$ \displaystyle\ \int { \dfrac{1}{(x^2+1)\sqrt{x^2-1}}} \mathrm{d}x $$ To know about the solution, visit my channel Calculus Society. I don't know what you would think about this, $$ \displaystyle\ \int { \dfrac{1}{\sec^2(x)+2\tan^2(x)}} \mathrm{d}x $$ or this, $$ \displaystyle\ \int { \dfrac{1}{1-\sin^4(x)}} \mathrm{d}x $$ Sorry I can't think of any more hard questions. Another simple one using integration by parts, $$ \displaystyle\ \int { \ln | x+\sqrt{1-x} | } \mathrm{d}x $$

Prajod
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