In this video I go over the method of integration by parts which allows the ability to simplify a more complex function to make integration easier. The integration by parts method corresponds to the product rule for derivatives in much the same way as the substitution rule corresponds to the chain rule for derivatives. This method is very important and is used throughout integral calculus so it is important to watch this video to fully understand the proof of it!
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Integration by Parts
Every differentiation rule has a corresponding integration rule. For instance, the Substitution Rule for integration corresponds to the Chain Rule for differentiation. (See my video on Substitution Rule)
The rule that corresponds to the Product Rule for differentiation is called Integration by Parts.
The Product Rule states that if f and g are differentiable functions, then
Now if we integrate both sides:
This is called the Formula for integration by parts.
We can simplify further by using the substitution rule:
