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.
We can revert to an expression involving the original variable x by recalling that u = 3x + 4, giving Z. cos(3x+4)dx =. 1. 3. sin(3x+4)+c. We have completed the integration by substitution. It is very easy to generalise the result ofthe previous example.