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My books states that the integrals like $\int \frac{\sin x}{x}dx$ and $\int e^{x^2}dx$ exist but they cannot be easily evaluated by elementary functions.I feel it is more because I am unable to evaluate it but can someone please tell me if there is a closed form for them?

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    http://en.wikipedia.org/wiki/Trigonometric_integral and http://en.wikipedia.org/wiki/Error_function should get you started.2012-07-23
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    See [this](http://math.stackexchange.com/questions/9199), [this](http://math.stackexchange.com/questions/155), and [this](http://math.stackexchange.com/questions/76650), for starters.2012-07-23
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    Possible duplicate of [Integration of Sinc function](http://math.stackexchange.com/questions/891812/integration-of-sinc-function)2016-03-03
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    @tired : I'm not sure that the given link is a duplicate. I don't think the OP asked for definite integrals, but rather for closed-form primitive functions. In my opinion the links given by J. M. are more relevant. There also is [this](http://math.stackexchange.com/q/830833) answer.2016-03-03

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