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If ∫ (6x + 7)/√((x−5)(x−4)) dx is written in the form A√(x² − 9x + 20) + B log|x + √(x² − 9x + 20) − 9/2| + C, then the values of A and B are

1. 6, 34
2. 3, 9
3. 12, 17
4. None of these

Correct answer: 6, 34

Solution

Note (x-5)(x-4)=x^2-9x+20=Q. d/dx[A sqrt(Q)] = A(2x-9)/(2 sqrt Q) and d/dx[B ln|x-9/2+sqrt Q|] = B/sqrt Q. So 6x+7 = A(2x-9)/2 + B. Matching: A=6, then -9(6)/2 + B = 7 => B=34. Thus A=6, B=34.

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