Suppose and . If , then the value of is…

MATHEMATICS · Subjective · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Suppose

A = \int \frac{dx}{x^2 + 6x + 25}

and

B = \int \frac{dx}{x^2 - 6x - 27}

. If

12(A + B) = \lambda \cdot \tan^{-1} \left( \frac{x+3}{4} \right) + \mu \cdot \ln \left| \frac{x-9}{x+3} \right| + C

, then the value of

(\lambda + \mu)

is .....