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Integration by Substitution

Integration by Substitution. If you cannot see the answer for integral by inspection, then the method of substitution is deployed. Example 1. Make dx the subject. Replace 2 x – 1 by u and write dx in terms of du. This was an easy question, you could have done it by inspection.

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Integration by Substitution

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  1. Integration by Substitution If you cannot see the answer for integral by inspection, then the method of substitution is deployed. Example 1 Make dx the subject Replace 2x – 1 by u and write dx in terms of du This was an easy question, you could have done it by inspection.

  2. Integration by substitution Example 2 Use the substitution u = sin x Make dx the subject This was also an easy question, you could have done it by inspection.

  3. Integration by substitution Integrals which are not so obvious. Example 3 Use the substitution u = x - 4 However, this integral can be found by using partial fractions.

  4. Integration by substitution Substitute x = u2 Example 4

  5. Integration by substitution Example 5 Substitute u2 = x + 1

  6. Integration by substitution Example 6 Substitute x = (u – 4)/3

  7. Integration by substitution Substitute x = 2sin u Example 7

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