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4 2 $begingroup$ Am I correct for pattern matching this integral? I have $$int frac{sqrt{9x^2+4}}{x^2}dx$$ Does this pattern match with: $$int frac{sqrt{a^2 + x^2}}{x^2}dx = -frac{a^2 + x^2}{x} + ln(x + sqrt{a^2 + x^2}) + c$$ If I factor out the 9, I get $$= 3 int frac{sqrt{x^2 + frac{4}{9}}}{x^2}$$ with $a = frac{2}{3}$ I get: $$3 left( - frac{sqrt{frac{4}{9}+x^2}}{x} + lnleft(x+sqrt{frac{4}{9}+x^2}right) +cright)$$ Is this the right track? Wolfram winds up with a different answer though: integration share | cite | improve this question edited 4 hours ago clathratus 4