Let
\[
f(x)=\int \frac{7x^{10}+9x^8}{(1+x^2+2x^9)^2}\,dx,\quad x > 0,
\]
and
\[
A=
\begin{bmatrix}
0 & 0 & 1 \\
\frac{1}{4} & f'(1) & 1 \\
\alpha & 4 & 1
\end{bmatrix}.
\]
If \( B=\operatorname{adj}(\operatorname{adj} A) \), then the value of \( \alpha \) for which \( \det(B)=1 \) is