$\mathop \smallint \nolimits_0^3 \,\,\frac{{3x\,\, + \,\,1}}{{{x^2}\,\, + \,\,9\;}}\;\,\,dx$ is equal to

$\log \,\,\left( {2\,\sqrt 2 } \right)\,\, + \,\,\frac{\pi }{2}$

$\log \,\,\left( {2\,\,\sqrt 2 } \right)\,\, + \,\,\frac{\pi }{6}$

$\log \,\,\left( {2\,\,\sqrt 2 } \right)\,\, + \,\,\frac{\pi }{3}$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

\int \nolimits_0^3 \,\,\frac{{3x\,\, + \,\,1}}{{{x^2}\,\, + \,\,9\;}}\;\,\,dx

is equal to

View answer and explanation

Correct option: A

\log \,\,(2\,\sqrt 2 )\,\, + \,\,\frac{\pi }{{12}}

Option A (

\log \,(2\sqrt 2 )\,+ \frac{\pi }{{12}}

) is correct because it results from correctly evaluating the definite integral after splitting it into two simpler integrals.