Generalized integral transformations

"Sarah Churchill (née Jenyns, spelt Jennings in most modern references), Duchess of Marlborough (5 June 1660 (old style) ? 18 October 1744) rose to be one of the most influential women of her time through her close friendship with Queen Anne of Great Britain. Sarah's friendship and influence with Princess Anne was widely known, and leading public figures often turned their attentions to her in the hope that she would influence Anne to comply with requests. As a result, by the time Anne became queen, Sarah?s knowledge of government, and intimacy with the Queen, had made her a powerful friend and a dangerous enemy."--Wikipedia.