A Level

MATHEMATICS · Single correct · A Level · Mathematics · Integration · Integration

Problem

∫(sin⁡θcos⁡3θ+sin⁡3θcos⁡9θ+sin⁡9θcos⁡27θ)dθ\int \left( \frac{\sin \theta}{\cos 3\theta} + \frac{\sin 3\theta}{\cos 9\theta} + \frac{\sin 9\theta}{\cos 27\theta} \right) d\theta is equal to (1) 12log⁡∣sec⁡27θsec⁡θ∣+C\frac{1}{2} \log \left| \frac{\sec 27\theta}{\sec \theta} \right| + C (2) 12log⁡∣sec⁡θsec⁡27θ∣+C\frac{1}{2} \log \left| \frac{\sec \theta}{\sec 27\theta} \right| + C (3) 12log⁡∣sec⁡27θ3sec⁡θ∣+C\frac{1}{2} \log \left| \frac{\sqrt[3]{\sec 27\theta}}{\sec \theta} \right| + C (4) None of these

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