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Question Number 18318 by tawa tawa last updated on 18/Jul/17

∫ ((x + sinx)/(cosx)) dx

$$\int\:\frac{\mathrm{x}\:+\:\mathrm{sinx}}{\mathrm{cosx}}\:\mathrm{dx} \\ $$

Commented by alex041103 last updated on 19/Jul/17

i think this is not elementary

$${i}\:{think}\:{this}\:{is}\:{not}\:{elementary} \\ $$

Commented by tawa tawa last updated on 19/Jul/17

please help.

$$\mathrm{please}\:\mathrm{help}. \\ $$

Commented by alex041103 last updated on 19/Jul/17

i think it is nom−elementary integral.  This means that the anti−derivitive  of the integrand cannot be expressed in terms of  elementary functions−powers,   exponentials, sums, logs, products and exetra.  For example∫((sin x)/x)dx is a  non−elementary functions.

$${i}\:{think}\:{it}\:{is}\:{nom}−{elementary}\:{integral}. \\ $$$${This}\:{means}\:{that}\:{the}\:{anti}−{derivitive} \\ $$$${of}\:{the}\:{integrand}\:{cannot}\:{be}\:{expressed}\:{in}\:{terms}\:{of} \\ $$$${elementary}\:{functions}−{powers},\: \\ $$$${exponentials},\:{sums},\:{logs},\:{products}\:{and}\:{exetra}. \\ $$$${For}\:{example}\int\frac{{sin}\:{x}}{{x}}{dx}\:{is}\:{a} \\ $$$${non}−{elementary}\:{functions}. \\ $$

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