dx x^2 + 4x + 13 is equal to - Vidyadip

MCQ

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

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

✓

Answer

Correct option: B.

$\frac{1}{3}{\tan ^{ - 1}}\left( {\frac{{x + 2}}{3}} \right) + c$

b
(b)$\int {\frac{{dx}}{{{x^2} + 4x + 13}} = \int {\frac{{dx}}{{{{(x + 2)}^2} + 9}} = \frac{1}{3}{{\tan }^{ - 1}}\frac{{(x + 2)}}{3} + c} } $.

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