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## Integration by Substitution

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**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.**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.**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.**Integration by substitution**Substitute x = u2 Example 4**Integration by substitution**Example 5 Substitute u2 = x + 1**Integration by substitution**Example 6 Substitute x = (u – 4)/3**Integration by substitution**Substitute x = 2sin u Example 7