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.
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, $$ \displaystyle\ \int { \ln | x+\sqrt{1-x} | } \mathrm{d}x $$