I think I'm missing something silly here, but I'm stuck in a rut - a push would be appreciated.
I'm working with this distribution
I want to find the mean and variance. Often it's easy to convert into something that looks like where is some pdf and therefore integrates to 1.
I didn't see a solution like this, so I went brute force and just tried to integrate it figuring it's probably not the most elegant way, but it should work.
using 'by parts':
I then try to do by parts again, but it's already clear that when I later go to evaluate the result between 0 and the first x^3 term will blow up and there aren't any other convenient x^3 terms to cancel it out later.