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.
So the integralZ2xâ1+x 2 dx is of the formZf(g(x))g â² (x)dxTo perform the integration we used the substitution u = 1 + x 2. In the general case it will beappropriate to try substituting u = g(x). Then du =dudxdx = g â² (x)dx.Once the substitution was made the resulting integral becameZâudu.