Evaluate (x+2) d x (x^ 2 +3 x+3 ) x+1

Mathematics · JEE Advanced · NTA Exams — Integral Calculus

1. \(\frac{2}{\sqrt{3}} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt{x+1}}{-x}\right)+c\)
2. \(\frac{2}{\sqrt{3}} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt{x+1}}{x}\right)+c\)
3. \(\frac{1}{\sqrt{3}} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt{x+1}}{-x}\right)+c\)
4. \(\frac{1}{\sqrt{3}} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt{x+1}}{x}\right)+c\)

Answer

(A) 2 3 ^ -1 ( 3 x+1 -x )+c

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