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If int (x^(2020)+x^(804)+x^(402))(2x^(16...

If `int (x^(2020)+x^(804)+x^(402))(2x^(1608)+5x^(402)+10)^(1//402)dx=(1)/(10a)(2x^(2010)+5x^(804)+10^(402))^(a//402)`. Then `(a-400)` is equal to .......

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Verified by Experts

The correct Answer is:
`96.5`
`int x(x^(2009)+x^(803)+x^(401))(2x^(1608)+5x^(402)+10)^(1//402) dx`
Put `2x^(2010)+5x^(804)+10x^(402)=t`,
`4020 (x^(2009)+x^(803) +x^(401))dx=dt`
`(x^(2009)+x^(803)+x^(401))dx=(dt)/4020`,
`=1/4020 int t^(1//402) dt =1/4020 (t^(1/402+1)/(1/402 +1))`
`=1/4020xx402/403 t^(403/402)`
`a=403`
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