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If f(x)=int(1)^(x)(logt)(1+t+t^(2))dt AA...

If `f(x)=int_(1)^(x)(logt)(1+t+t^(2))dt AAxge1`, then prove that `f(x)=f(1/x)`.

Text Solution

Verified by Experts

The correct Answer is:
NA
Given `f(x)=int_(1)(x)(logt)/(1+t+t^(2))dt`
or `f(1/x)=int_(1)^(1//x)(logt)/(1+t+t(2))dt`
Let `y=1/t` or `dy=(dt)/(t^(2))`
`:. f(1/x)=int_(1)^(x)("log"1/y)/(1+1/y+1/(y^(2)))(-1/(y^(2))dy)`
`=int_(1)^(x)(logy)/(1+y+y^(2))dy=f(x)`
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