\[\displaystyle \sum _{ i=1 }^{ 6 }{ \left( \arcsin ( { x }_{ i } ) +\arccos ( { y }_{ i } ) \right) } =9\pi \]

If the above equation satisfies, then find the value of

\[ \displaystyle \int \limits_{ \displaystyle \sum _{ i=1 }^{ 6 }{ { x }_{ i } } }^{ \displaystyle \sum _{ i=1 }^{ 6 }{ { y }_{ i } } }{ x\ln { (1+{ x }^{ 2 }) } } \left( \frac { { e }^{ x } }{ 1+{ e }^{ 2x } } \right) \ \mathrm{d}x \]

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