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int1/(x^2(x^4+1)^(3/4))dx...

`int1/(x^2(x^4+1)^(3/4))dx`

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` int(1)/(x^(2)(x^(4)+1)^(3//4))dx`
` =int(1)/(x^(2){x^(4)(1+(1)/(x^(4)))}^(3//4))dx`
` =int(1)/(x^(5)(1+(1)/(x^(4)))^(3//4))dx`
`" Let " 1+(1)/(x^(4)) =trArr (-4)/(x^(5)) =dt rArr (1)/(x^(5)) dx=(dt)/(4)`
`=int (1)/(t^(3//4)) .(dt)/(-4) =-(1)/(4) .int t^(-3//4) dt`
`=-(1)/(4).(t^(1//4))/(1//4)+C`
`=-(1+(1)/(x^(4)))^(1//4)+C`
`=-((x^(4)+1)/(x))^(1//4)+C`
`=-(1)/(x)(x^(4)+1)^(1//4)+C`
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