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Evaluate: int(x^4+1)/(x^6+1)dx...

Evaluate: `int(x^4+1)/(x^6+1)dx`

Text Solution

Verified by Experts

The correct Answer is:
` "tan"^(-1)(x-(1)/(x))-(2)/(3)tan^(-1)(x^(3))+C`
`I=int(x^(4)+1)/(x^(6)+1)dx=int((x^(2)+1)^(2)-2x^(2))/((x^(2)+1)(x^(4)-x^(2)+1))dx`
`=int(x^(2)+1)/(x^(4)-x^(2)+1)dx-2int(x^(2)dx)/((x^(6)+1))`
`=int(1+(1)/(x^(2)))/(x^(2)-1+(1)/(x^(2)))dx-2int(x^(2)dx)/((x^(3))^(2)+1)`
`="tan"^(-1)(x-(1)/(x))-(2)/(3)tan^(-1)(x^(3))+C`
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