The integral of tangent is $\ln(\sec(x))$ so I was thinking that the answer is $\ln(\sec(e^x))$ but the derivative of that is $e^x\ln(\sec(x))$ so that would not be the correct answer. So what is the integral of $\tan(e^x)$?
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3There is no closed form (Wolfram Alpha). Many integrals do not have closed forms, and even if a similar looking integral has a closed form, that doesn't guarantee a closed form for the original integral. – Toby Mak Sep 14 '19 at 01:02
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Is there any way to prove that? – Asher Ross Sep 14 '19 at 01:15
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It is very difficult to prove that no closed form exists. However, here are some possible strategies that people use to prove this. – Toby Mak Sep 14 '19 at 01:17