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Evaluate for m in N , int(x^(3m)+x^(2n...

Evaluate for `m in N ,` `int(x^(3m)+x^(2n)+x^m)(2x^(2m)+3x^m+6)^(1/m)dx ,x >0`

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`I=int(x^(3m)+x^(2m)+x^(m))(2x^(2m)+3x^(m)+6)^(1//m)dx`
`=int((x^(3m)+x^(2m)+x^(m))/(x))(x)(2x^(2m)+3x^(m)+6)^(1//m)dx`
`=int(x^(3m-1)+x^(2m-1)+x^(m-1))(2x^(3m)+3 x^(2m)+6x^(m))^(1//m)dx`
Let `2x^(3m)+3x^(2m)+6x^(m)=t." Them " dt=6m(x^(3m-1)+x^(2m-1)+x^(m-1))dx.`
` :. I=intt^(1//m)(dt)/(6m)=(1)/(6m)(t^((1)/(m)+1))/((1)/(m)+1)+C`
`=(1)/(6(m+1))(2x^(3m)+3x^(2m)+6x^(m))^((m+1)//m)+C`
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