(1+x) x (x^ 2 +2 x ) ^ 2 x-(1+x) 2 x d x = 1 2 _ e | t+1 t-1 |+c where t is

Mathematics · JEE Advanced · NTA ExamsIntegral Calculus

\(\int \frac{(1+x) \sin x}{\left(x^{2}+2 x\right) \cos ^{2} x-(1+x) \sin 2 x} d x\)\(=\frac{1}{2} \log _{e}\left|\frac{t+1}{t-1}\right|+c\)
where t is
  1. (x + 1) cos x – sin x
  2. (x + 1) sin x – cos x
  3. (x + 1) sin x + cos x
  4. (x + 1) cos x + sin x

Answer

(A) (x + 1) cos x – sin x

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