Mathematics · JEE | INTEGRALS

Consider the following statements regarding the integration of rational functions using partial fractions:\n(A) The integrand \( \frac{3\sin\phi - 2}{5 - \cos^2\phi - 4\sin\phi} \) can be transformed by substituting \( y = \sin\phi \).\n(B) The partial fraction decomposition of \( \frac{x^2 + x + 1}{(x^2 + 1)(x + 2)} \) is of the form \( \frac{A}{x+2} + \frac{Bx+C}{x^2+1} \).\n(C) When resolving \( \frac{x^2}{(x^2+1)(x^2+4)} \), we substitute \( y = x^2 \) directly in the partial fraction step without integrating immediately.\n(D) The integral \( \int \frac{dx}{x(x^4-1)} \) can be evaluated by multiplying numerator and denominator by \( x^3 \).\nWhich of the above statements are correct?

1. A
   (A), (B) and (C) only
2. B
   (A), (B), (C) and (D)
3. C
   (B) and (D) only
4. D
   and (C) only