Here, I have attached my try work below. Though I am stuck in integration, but I would like some physics people to answer it. 

Can I treat the $y\sin\theta$ factor to be constant while doing integration of $r$, as $y$ is also a fixed radial distance and later integrate $\theta$ while $r$ is done?

And If a better method is available to do such potential calculations, please suggest it.

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[1]: https://i.sstatic.net/9BRbE.jpg