The gallbladder is a small pouch that sits just under the liver. The gallbladder stores bile produced by the liver. After meals, the gallbladder is empty and flat, like a deflated balloon.efore a meal, the gallbladder may be full of bile and about the size of a small pear. In response to signals, the gallbladder squeezes stored bile into the small intestine through a series of tubes called ducts. Bile helps digest fats, but the gallbladder itself is not essential.
U-substitution is for functions that can be written as the product of another function and its derivative. $$\int u du$$. Integration by parts is for functions that can be written as the product of another function and a third function's derivative.
I've never heard of monotonic being used for two (input) variables, but I suppose it would mean that, for each fixed value of y, u is a monotonic function of x, and for each fixed value of x, u is a monotonic function of y (and I expect they'd need to be either both monotonic increasing or both monotonic decreasing).