JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Analyzing +4 | -1

\int {\frac{{\cos \theta }}{{5 + 7\sin \theta - 2{{\cos }^2}\theta }}} \,d\theta \,\, = A\,\,{\log _e}\left| {B(\theta )} \right| + C,

where

C

is constant of integration, then

\frac{{B(\theta )}}{A}

can be

View answer and explanation

Correct option: D

\frac{{5(2\sin \theta + 1)}}{{\sin \theta + 3}}

Option D is correct because after integrating the given expression and simplifying, the result matches the form

A \log_e |B(\theta)| + C

, leading to the correct value of

\frac{{B(\theta)}}{A}

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