I want to find \begin{align}(1-p)\log\left [\int^{\infty}_{0} [f(x)]^pdx\right],\end{align} given that $\alpha,\beta, \theta$ and $p$ are constants and \begin{align} f(x)=\dfrac{ \frac{ \theta\alpha \beta}{x^2}\left( 1+\frac{ \beta}{x} \right) ^{-(1-\alpha)} }{\Big\{ 1-(1-\theta)\left[1-\left( 1+\frac{ \beta}{x} \right) ^{-\alpha} \right] \Big\}^2},\;x\in\Bbb{R}\end{align}
MY TRIAL
By substitution, let $u=1+\frac{ \beta}{x}, $ then $du=-[(u-1)^2/\beta]dx$ \begin{align} f(u)&=\dfrac{ \frac{ \theta\alpha }{\beta}(u-1)^2u ^{-(1-\alpha)} }{\Big\{ 1-(1-\theta)\left[1-u ^{-\alpha} \right] \Big\}^2}\\&=\dfrac{ \frac{ \theta\alpha }{\beta}(u-1)^2u ^{-(1-\alpha)} }{ 1-2(1-\theta)\left[1-u ^{-\alpha} \right]+(1-\theta)^2\left[1-u ^{-\alpha} \right] ^2}\end{align} I'm stuck here, please, how do I continue?