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Deduce the reduction formula for I(n)=in...

Deduce the reduction formula for `I_(n)=int(dx)/(1+x^(4))^(n)` and Hence evaluate `I_(2)=int(x)/(1+x^(4))^(2)`.

Text Solution

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`I_(n)=x/((4(n-1)(1+x^(4))^(n-1))+(4n-5)/(4(n-1))I_(n-1)`
`I_(2)=x/(4(1+x^(4)) + (1/(2sqrt(2))tan^(-1)(x-1/x)/sqrt(2) -1/(4sqrt(2))"ln"(x+1/x-sqrt(2))/(x+1/x+sqrt(2)))+C`
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