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I have the following definite integral: $$I=\int_{-2}^{1}-\frac{4}{2x^3 \cos{x}+2}\ \mathrm dx.$$

The approximate value of the integral is $-7.14725$. Neither Mathematica, nor Wolfram Alpha could not find a closed form, and I have no idea how to proceed. Does a closed form exist, even one using non elementary functions?

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    $\begingroup$ Why didn't you write $$I=-\int_{-2}^{1}\frac{2}{x^3 \cos{x}+1}\ \mathrm dx\ ?$$ $\endgroup$ – Sophie Agnesi Jun 9 '16 at 2:26
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    $\begingroup$ I would be surprised by a closed form. $\endgroup$ – Claude Leibovici Jun 9 '16 at 6:25
  • $\begingroup$ Why do you need a closed form? $\endgroup$ – Yuriy S Aug 18 '16 at 14:02

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