\hspace{-16}\bf{\int_{-1}^{1}\frac{2x^{1004}+x^{3014}+x^{2008}.\sin(x)^{2007}}{1+x^{2010}}dx}
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1since sin is odd function,
\begin{align*} & \mathbb{I} = 2\int_{0}^{1} \frac{x^{1004}}{1+x^{2010}} + x^{1004} \\ &= 2[ \frac{\tan ^{-1}(x^{1005})}{1005} +\frac{x^{1005}}{1005} ]\\ &= \frac{2}{1005}[\frac{\pi}{4}+1] \\ & \bullet \bullet \bullet \bullet \\ & \\ & \\ & \\ & \\ & \\ & \end{align*}
