AP EAMCET · Maths · Indefinite Integration
\(\int \frac{2-\sin x}{2 \cos x+3} d x=\)
- A \(\frac{2}{\sqrt{5}} \tan ^{-1}\left(\frac{1}{\sqrt{3}} \tan \frac{x}{2}\right)-\log \sqrt{2 \cos x+3}+c\)
- B \(\frac{4}{\sqrt{5}} \tan ^{-1}\left(\frac{1}{\sqrt{5}} \tan \frac{x}{2}\right)+\log \sqrt{2 \cos x+3}+c\)
- C \(\frac{3}{\sqrt{5}} \tan ^{-1}\left(\frac{1}{\sqrt{5}} \tan \frac{x}{2}\right)+\log \sqrt{2 \cos x+3}+c\)
- D \(\frac{1}{\sqrt{5}} \tan ^{-1}\left(\frac{1}{\sqrt{5}} \tan \frac{x}{2}\right)-\log \sqrt{2 \cos x-3}+c\)
Answer & Solution
Correct Answer
(B) \(\frac{4}{\sqrt{5}} \tan ^{-1}\left(\frac{1}{\sqrt{5}} \tan \frac{x}{2}\right)+\log \sqrt{2 \cos x+3}+c\)
Step-by-step Solution
Detailed explanation
\(\mathrm{I}=\int \frac{2-\sin x}{2 \cos x+3} d x\)…
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