in this section, we will begin investigating some more advanced techniques for integration –...
TRANSCRIPT
In this section, we will begin investigating some more advanced techniques for integration – specifically, integration by parts.
Section 8.1 Integration By Parts
Idea
Integration by Parts is essentially a product rule for antidifferentiation.
It comes from the product rule from derivatives, as we will see in the proof of the theorem.
TheoremIntegration by Parts
If u and v are differentiable functions, then
1.
2.
Choosing u and dv
dv should be selected so that v can be found by antidifferentiating
Also, should be simpler to work with than the original integral.
!!! Do not forget to consider a variable substitution before using any more advanced technique.
Choosing u and dv
L I A T E
Choose u in this order:
L = logarithm
I = inverse trigonometry
A = algebraic functions
T = trigonometric functions
E = exponential functions
dv = rest of the original integrand
Example 1
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Example 2
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Example 3
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Example 4
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Example 5
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Example 6
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Example 7
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Example 8
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Example 9
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