\(\int {\frac{{dx}}{{(\sin x + 4)(\sin x - 1)}} = \frac{A}{{\tan \frac{x}{2} - 1}} + B{{\tan }^{ - 1}}} \left( {f(x)} \right) + c\), then
1
\(A = \frac{1}{5}\), \(B = -\frac{2}{{5\sqrt {15} }}\), \(f(x) = \frac{{4\tan x + 3}}{{\sqrt {15} }}\)
2
\(A = \frac{-1}{5}\), \(B = \frac{1}{{\sqrt {15} }}\), \(f(x) = \frac{{4\tan \left( {\frac{x}{2}} \right) + 1}}{{\sqrt {15} }}\)
3
\(A = \frac{2}{5}\), \(B = -\frac{2}{{5\sqrt {15} }}\), \(f(x) = \frac{{4\tan\frac{x}{2} + 1}}{{\sqrt {15} }}\)
4
\(A = \frac{2}{5}\), \(B = -\frac{2}{{\sqrt {15} }}\), \(f(x) = \frac{{4\tan \left( {\frac{x}{2}} \right) + 1}}{{\sqrt {5} }}\)