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If x=int(0)^(oo)(dt)/((1+t^(2))(1+t^(201...

If `x=int_(0)^(oo)(dt)/((1+t^(2))(1+t^(2017)))`, then `(3x)/(pi)` is equal to

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Verified by Experts

The correct Answer is:
`00000.75`
`00000.75`
Put `t=tantheta`
`implies int_(0)^(pi//2) (sec^(2)theta d theta)/(sec^(2) theta (1+tan^(2017)theta))=(pi)/4`
`implies(3x)/(pi)=3/4=0.75`
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