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int0^1(x^5(4-x^2))/sqrt(1-x^2)dx...

`int_0^1(x^5(4-x^2))/sqrt(1-x^2)dx`

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`int_0^1(x^5(4-x^2))/sqrt(1-x^2)dx`
=`int_0^(pi/2)(sin^5theta(4-sin^2theta))/costheta.costhetad theta` (where `x=sintheta`
`rArr dx=costhetad theta`)
=`4int_0^(pi/2)sin^5thetad theta-int_0^(pi/2)sin^7thetad theta`
=`4 cdot 4/5 cdot 2/3 - 6/7 cdot 4/5 cdot 2/3`
=`8/15(4-6/7)=8/15cdot22/7=(176)/105`
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