\(\int\frac{dx}{x^2+4x+13}=\)
A. \(\frac13\tan^{-1}\left(\frac{x+2}{3}\right)+C\)
B. \(\frac19\tan^{-1}\left(\frac{x+2}{3}\right)+C\)
C. \(\tan^{-1}\left(\frac{x+2}{3}\right)+C\)
D. \(\frac13\tan^{-1}\left(\frac{x-2}{3}\right)+C\)
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Answer: A. \(\frac13\tan^{-1}\left(\frac{x+2}{3}\right)+C\)
\(x^2+4x+13=(x+2)^2+3^2\); use \(\int\frac{dx}{u^2+a^2}=\frac1a\tan^{-1}\frac ua\).
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· 23 Oct 2026
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