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

$\log \,\,\left( {{x^2} + \,\,4x + 13} \right)\,\, + \,\,c$

$\log \,\,\left( {2x\,\, + \,\,4} \right)\,\, + c$

${{{\left( {{x^2} + \,\,4x\,\, + 13} \right)}^2}}$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\int \frac{{dx}}{{{x^2}\,\, + \,\,4x\,\, + \,\,13}}

is equal to

View answer and explanation

Correct option: B

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

Option B (

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

) is correct because it is the result of integrating the given expression by completing the square.