MathematicsMedium64×since 2004Q4022If ∫cosθ5+7sinθ−2cos2θdθ\int {{{\cos \theta } \over {5 + 7\sin \theta - 2{{\cos }^2}\theta }}} d\theta∫5+7sinθ−2cos2θcosθdθ = Aloge∣B(θ)∣+C{\log _e}\left| {B\left( \theta \right)} \right| + Cloge∣B(θ)∣+C, where C is a constant of integration, then B(θ)A{{{B\left( \theta \right)} \over A}}AB(θ) can be :A2sinθ+15(sinθ+3){{2\sin \theta + 1} \over {5\left( {\sin \theta + 3} \right)}}5(sinθ+3)2sinθ+1B2sinθ+1sinθ+3{{2\sin \theta + 1} \over {\sin \theta + 3}}sinθ+32sinθ+1C5(2sinθ+1)sinθ+3{{5\left( {2\sin \theta + 1} \right)} \over {\sin \theta + 3}}sinθ+35(2sinθ+1)D5(sinθ+3)2sinθ+1{{5\left( {\sin \theta + 3} \right)} \over {2\sin \theta + 1}}2sinθ+15(sinθ+3)Check answerSkip