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I learnt this from Krizalid aka the Inte-Killer. Try the substitution u = 1/x.
I wouldn't be surprised if Kriz has another clever substitution.
Trigonometric substitution, is a way.
Another way is below.
I assume that ,
Let , then and
Applying the substitution gives us
For , the integral is .
So we can say that, for any x, the integral is
I thought I'd elaborate more on my post.
Now it became a matter of simple substition ( ).
Another approach . . .
Substitute: . . .
We had: .
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