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

Question

If ∫ ( 2 x + 1 ) 6 ( 3 x + 2 ) 8 d x = P 2 x + 1 3 x + 2 Q + R , then P Q =, 1 7 2, 1 7, 7 2, 4

MARKS App · Accepted Answer

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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