If$\int { \left( { x }^{ 2010 }+{ x }^{ 804 }+{ x }^{ 402 } \right) } ({ {2 x }^{ 1608 }+{5 x }^{ 402 }+10 })^{ \frac { 1 }{ 402 } }dx=\frac { 1 }{ 10k } ({ { 2x }^{ 2010 }+{ 5x }^{ 804 }+{ 10x }^{ 402 }) }^{ \frac { k }{ 402 } }+C$.Find sum of digits of k?

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