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Integrate the functions(3x^2)/(x^6+1)...

Integrate the functions`(3x^2)/(x^6+1)`

Text Solution

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`int 3x^2dx /(x^6+1)`
`=int 3x^2dx/((x^3)^2+1) `
`t=x^3 implies dt=3x^2dx`
`int dt/t^2+1`
=` tan^-1t+C ` where c is the constant of integration.`=tan^-1(x^3)+C `where `t=x^3`
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