TS EAMCET · Maths · Indefinite Integration
\(\int \frac{1+\sqrt{3} \cot x}{1-\sqrt{3} \cot x} d x=\)
- A \(-\frac{x}{2}+\frac{\sqrt{3}}{2} \log \left|\sin \left(x-\frac{\pi}{3}\right)\right|+c\)
- B \(\frac{x}{2}+\frac{\sqrt{3}}{2} \log \left|\sin \left(x-\frac{\pi}{3}\right)\right|+c\)
- C \(-\frac{x}{2}-\frac{\sqrt{3}}{2} \log \left[\sin \left(x-\frac{\pi}{3}\right)\right]+c\)
- D \(\frac{x}{2}-\frac{\sqrt{3}}{2} \log \left|\sin \left(x-\frac{\pi}{3}\right)\right|+c\)
Answer & Solution
Correct Answer
(A) \(-\frac{x}{2}+\frac{\sqrt{3}}{2} \log \left|\sin \left(x-\frac{\pi}{3}\right)\right|+c\)
Step-by-step Solution
Detailed explanation
\(\int \frac{1+\sqrt{3} \cot x}{1-\sqrt{3} \cot x} d x=\int \frac{\tan x+\sqrt{3}}{\tan x-\sqrt{3}} d x\)…
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