Try the addition of the vertical ellipse solid and the solid rotated by the straight line, with the bounds x=3-5 or y=0-5, however your approach is (slices or shells)
Curious on where you got thequestion from
Wolfram can't be correct IMO. I think integration by parts will do it
Yep I thought so, harrisony didn't type in the thing correctly. It looks like you have to do integration by parts at least twice