# integrating a tricky function $\int\sec^3x\ln (\arctan e^x)dx$

I want to integrate the flowing $$\int\sec^3x\ln (\arctan e^x)dx$$ i tried u substitution using $u=e^x$ and $\arctan e^x=u$ and also $\sec^3x=u$, but i found nothing. What would you suggest?

• Have you tried integration by parts? – Maryam Dec 26 '15 at 17:56
• @Maryam yes i did – zakaria hmimid Dec 26 '15 at 17:56
• I don't think this has an elementary antiderivative. – Chappers Dec 26 '15 at 17:58
• @Chappers .. but the function is continous so it has one .. – zakaria hmimid Dec 27 '15 at 12:39
• It has an antiderivative. But not an antiderivative composed of a finite combination of elementary functions, which is what an elementary antiderivative is. See the links in @Lucian's answer. – Chappers Dec 27 '15 at 16:20