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If $\int (\frac{4 e^{x} + 6 e^{- x}}{9 e^{x} - 4 e^{- x}}) dx = Ax + Blog |(9 e^{2 x} - 4)| + C, then (A, B) =$

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$(\frac{3}{2}, \frac{- 35}{36})$

$(\frac{3}{2}, \frac{35}{36})$

$(\frac{- 3}{2}, \frac{- 35}{36})$

$(\frac{- 3}{2}, \frac{35}{36})$

answer is C.

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Detailed Solution

$= \int (\frac{4 e^{x} + 6 e^{- x}}{9 e^{x} - 4 e^{- x}}) dx$

$4 e^{2 x} + 6 = A (9 e^{2 x} - 4) + B (18 e^{2 x})$

Comparing the coefficients on both sides

$A = - \frac{3}{2} and B = \frac{35}{36}$

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