Hi, for my private repos in BitBucket I'm currently using Shippable.
Setup is easy and tests run quickly. The service is young and it might happen that the build stucks. However their customer support is very good and they generally answer quickly. Furthermore the free account let you have up to 5 private repos.
Another good service seems to be Drone, but I haven't tried it.
Good luck!
You can try shippable, following tutorial can help you in setting up laravel project in shippable - http://viveksoni.net/shippable-continues-integration-php-laravel-5-2/
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