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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.

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

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

Uroš Kosmač
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