Evaluate the integral of arctan(1/x)

We will use substitution for the partial integration:
The integral becomes:=
2nd integration:
we will add and subtract x^2 to the numerator:
u-substitution:
...=
Finally:...=

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Answerthe simplified expression isexplanationthe given expression is,let us deal with the bracket first.the two negatives in the parenthesis will become positive.the expression now becomes,we now expand the parenthesis to get,we group like terms to obtain,this simplifies to,