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AP EAMCET202120 Aug 2021Morning ShiftMathematicsIndefinite IntegrationActual

If ∫ ( 2 x + 1 ) 6 ( 3 x + 2 ) 8 d x = P 2 x + 1 3 x + 2 Q + R , then P Q =

Options

  1. A1 7 2
  2. B1 7
  3. C7 2
  4. D4

Correct answer

A. 1 7 2

Step-by-step solution

Given, ∫ ( 2 x + 1 ) 6 ( 3 x + 2 ) 8 d x = P 2 x + 1 3 x + 2 Q + R Put t = 2 x + 1 3 x + 2 ⇒ d t d x = 3 x + 2 2 - 2 x + 1 3 3 x + 2 2 ⇒ d t = d x 3 x + 2 2 ∴ ∫ ( 2 x + 1 ) 6 ( 3 x + 2 ) 8 d x = ∫ t 6 d t ∫ t 6 d t = t 7 7 + C = 1 7 2 x + 1 3 x + 2 7 + C ⇒ P = 1 7 ,   Q = 7   &   R = C ∴ P Q = 1 7 7 = 1 7 2

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