1.
Let the domain of the function
f(x)=log⁡4(log⁡5(log⁡3(18x−x2−77)))f(x)=\log_4\left(\log_5\left(\log_3(18x-x^2-77)\right)\right)
be (a,b)(a,b). Then the value of the integral
∫absin⁡3xsin⁡3x+sin⁡3(a+b−x) dx\int_a^b \frac{\sin^3 x}{\sin^3 x+\sin^3(a+b-x)}\,dx
is equal to: