If $\smallint \,\,\frac{{dx}}{{5 + 4\,\,\cos \,\,x}} = A\,\,{\tan ^{ - 1}}\left( {B\,\,\tan \,\,x/2} \right)\,\, + \,\,C$, then

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

\int \,\,\frac{{dx}}{{5 + 4\,\,\cos \,\,x}} = A\,\,{\tan ^{ - 1}}\left( {B\,\,\tan \,\,x/2} \right)\,\, + \,\,C

, then

View answer and explanation

Correct option: B

A = 2/3,\;\,B = 1/3

Option B (

A = 2/3,\;\,B = 1/3

) is correct because after applying trigonometric substitutions and integrating, the values of A and B match the given form.

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