An effective method of integration is integration by algebraic substitution. In this type of problem dy⁄dx can be treated like a fraction.
The key to recognising this type of integration is that one part of the expression to be integrated is often the derivative of another part. Make sure that x is totally removed from the substituted integral.
The best way to illustrate integration by substitution is by six examples of some of the different methods.
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Example 1
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Example 2
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Example 3
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| Find ∫ (3x − 7)5 dx | Find ∫ x(x − 3)4 dx | Find ∫ x √(x2 + 9) dx |
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Example 4
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Example 5
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Example 6
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| Find ∫ 8ex4. x3 dx | Find |
Find  |
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"Although each example has a similar substitution, each has its own particular features and as always, practice makes perfect!"
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