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| Integration by Substitution |
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| Put g(x) = t |
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| Differentiating g(x) with respect to t, we have |
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| g'(x) dx = dt |
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 F(t) + C |
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 F(g(x)) + C |
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| Note 1: |
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| Note 2: |
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| Example: |
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| Suggested answer: |
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| Put tanx = t such that sec2xdx = dt |
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| When the integrand consists of trigonometric function, we use suitable trigonometric identities to simplify the function so that it can be integrated. Few identities are given below for ready reference. |
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(1)  |
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(2)  |
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(3)  |
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(4)  |
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(5)  |
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(7)  |
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(8)  |
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| Example: |
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| Integrate the function sinx. sin2x sin3x. |
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| Suggested answer: |
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