A dozen integrals: Russell-style

On June 15, 1876, the Proceedings of the Royal Society of London published a paper by Mr. W. H. L. Russell entitled "On certain integrals". The paper starts with "The following are certain integrals which will, I hope, be found interesting". The rest of the paper is simply a list of 12 integrals. We provide a list of 12 integrals that we hope would be interesting.