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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. Let Replace: Now it became a matter of simple substition ( ).
Hello, Apprentice123! Another approach . . . Let: Substitute: . . . Let Substitute: . Back-substitute: . We had: . Answer: .
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