Question

$ \int{\frac{dx}{{{x}^{2}}+4x+13}} $ is equal to

• A. $ \log ({{x}^{2}}+4x+13)+c $
• B. $ \frac{1}{3}{{\tan }^{-1}}\left( \frac{x+2}{3} \right)+c $
• C. $ \log (2x+4)+c $
• D. $ \frac{2x+4}{({{x}^{2}}+4x+13)}+c $

Answer 1

Answer: (B)

Let $ I=\int{\frac{dx}{4{{x}^{2}}+4x+13}} $
$ =\int{\frac{dx}{{{x}^{2}}+4x+4+9}} $
$ =\int{\frac{dx}{{{(x+2)}^{2}}+{{3}^{2}}}} $
$ =\frac{1}{3}{{\tan }^{-1}}\left( \frac{x+2}{3} \right)+c $