$$ \begin{aligned} & \text { If } \int \frac{x^2-x+2}{x^2+x+2} d x=x-\log (f(x))+\frac{2}{\sqrt{7}} \tan ^{-1}(g(x))+c, \text { then } \\ & f(-1)+\sqrt{7} g(-1)= \end{aligned} $$

$$ \int \sec \left(x-\frac{\pi}{3}\right) \sec \left(x+\frac{\pi}{6}\right) d x= $$

If $\int \frac{a \cos x+3 \sin x}{5 \cos x+2 \sin x} d x=\frac{26}{29} x-\frac{k}{29} \log |5 \cos x+2 \sin x|+\ldots$ then $|a+k|=$

If $\int \frac{d x}{1-\sin ^4 x}=A \tan x+B \tan ^{-1}(\sqrt{2} \tan x)+C$, then $A^2-B^2=$