\int \frac{2- \sin x}{2 \cos x+3} \dx= [AP EAPCET 20 May 2024 Shift 2]

Correct Answer is : 4√5Tan−1(1√5tanx2)+log√2cosx+3+c

{2}/{\sqrt{5}} {\Tan}^{-1} ( {1}/{\sqrt{3}} \tan \frac{x}{2}) -\log \sqrt{2 \cos x+3}+c

{4}/{\sqrt{5}} {\Tan}^{-1} ( {1}/{\sqrt{5}} \tan \frac{x}{2}) +\log \sqrt{2 \cos x+3}+c

{3}/{\sqrt{5}} {\Tan}^{-1} ( {1}/{\sqrt{5}} \tan \frac{x}{2}) +\log \sqrt{2 \cos x-3}+c

{1}/{\sqrt{5}} {\Tan}^{-1} ( {1}/{\sqrt{5}} \tan \frac{x}{3}) -\log \sqrt{2 \cos x-3}+c

Indefinite Integration

Section: Mathematics

Question : 71 of 89

Marks: +1, -0

∫‌

2−sin‌x

2‌cos‌x+3

‌dx=

[AP EAPCET 20 May 2024 Shift 2]

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