A) \[\log ({{x}^{2}}+4x+130)+c\]
B) \[\frac{1}{3}{{\tan }^{-1}}\left( \frac{x+2}{3} \right)+c\]
C) \[\log (2x+4)+c\]
D) \[\frac{1}{{{x}^{2}}+4x+13}+c\]
E) \[\frac{2x+4}{{{({{x}^{2}}+4x+13)}^{2}}}+c\]
Correct Answer: B
Solution :
Let \[I=\int{\frac{dx}{{{x}^{2}}+4x+13}}\] \[=\int{\frac{dx}{{{x}^{2}}+4x+4+{{3}^{2}}}}=\int{\frac{dx}{{{(x+2)}^{2}}+{{3}^{2}}}}\] \[=\frac{1}{3}{{\tan }^{-1}}\left( \frac{x+2}{3} \right)+c\]
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