AP EAMCET · Maths · Indefinite Integration
\(\int \frac{\operatorname{cosec} x}{3 \cos x+4 \sin x} d x=\)
- A \(\frac{1}{2} \log \left|\frac{\cos x}{3 \sin x+4 \cos x}\right|+c\)
- B \(\frac{1}{3} \log \left|\frac{\sin x}{3 \cos x+4 \sin x}\right|+c\)
- C \(\frac{1}{3} \log \left|\frac{3 \cos x+\sin x}{3 \cos x+4 \sin x}\right|+c\)
- D \(\frac{1}{2} \log \left|\frac{\cos x+4 \sin x}{3 \cos x+4 \sin x}\right|+c\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{3} \log \left|\frac{\sin x}{3 \cos x+4 \sin x}\right|+c\)
Step-by-step Solution
Detailed explanation
Let \(\mathrm{I}=\int \frac{\operatorname{cosec} x}{3 \cos x+4 \sin x} d x\) \(=\int \frac{\operatorname{cosec}^2 x}{3 \cot x+4} d x\), Let \(3 \cot x+4=t\)…
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