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I=∫0∞x4(1+x4)2 dx\large I = \int_{0}^{\infty} \dfrac{x^{4}}{(1+x^{4})^{2}} \, dxI=∫0∞(1+x4)2x4dx
If the value of the integral above is of the form πbc\dfrac{\pi}{b\sqrt{c}}bcπ, where bbb, ccc are integers and ccc is square-free, find the value of 10b+c10b+c10b+c.
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