Given that ∫(3 cos x + 4 sin x)/(2 cos x + 5 sin x) dx = (αx)/29 + (β/29) ln|2 cos x + 5 sin x| + c. What is the value of β?

From the decomposition 3 cos x + 4 sin x = A(2 cos x + 5 sin x) + B(d/dx of denominator) = A(2 cos x + 5 sin x) + B(-2 sin x + 5 cos x). Comparing: 3 = 2A + 5B and 4 = 5A - 2B. Solving these equations gives A = 26/29 and B = 7/29. The integral evaluates to (26x)/29 + (7/29) ln|2 cos x + 5 sin x| + c. Hence β = 7.