I tried many ways to evaluate the below integral but i didn't succeed , I have used Hypergeometric functions but it fails , now My question is the below integral has known closed form ? and how i can evaluate it ?
$$\int_{e}^{\pi} \frac{dx}{4(x^2-1)- (x^2-1)^{\frac14}2^{-\frac14 }}$$
Note Wolfram alpha show that is a positive integrand as shown here