So, I'm stuck with an integral. It asks- $$ \int e^x \sec(x) dx $$

I tried integration by parts, tried substituting. Nothing worked. Wolframalpha gave me some peculiar stuff(something called 'Hypergeometric function') which I don't understand at all.

Any kind of help will be appreciated. Thank you.

  • 1
    $\begingroup$ If Wolfram Alpha gives a hypergeometric function, presumably there is no elementary antiderivative. You can't integrate everything. $\endgroup$
    – saulspatz
    Jan 4, 2020 at 18:37
  • $\begingroup$ "seemingly" ??? The number of characters has no relation to the difficulty :-) Try $x^x$. $\endgroup$
    – user65203
    Jan 4, 2020 at 20:04
  • $\begingroup$ A hypergeometric $\phantom{}_2 F_1$ with complex parameters, hmm, such a joy! :D $\endgroup$ Jan 4, 2020 at 22:11

1 Answer 1


As it happens, this is a non-elementary integral, but you can solve it in terms of Hypergeometric function, but it's quite messy.


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