Example 8 - Find integrals (i) dx / x2 - 16 - Chapter 7 - Examples

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  1. Chapter 7 Class 12 Integrals
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Example 8 Find the following integrals: (i) ﷮﷮ 𝑑𝑥﷮ 𝑥﷮2﷯ −16﷯﷯ ﷮﷮ 𝑑𝑥﷮ 𝑥﷮2﷯ −16﷯﷯ = ﷮﷮ 𝑑𝑥﷮ 𝑥﷮2﷯ − 4﷮2﷯﷯﷯ = 1﷮2 × 4﷯𝑙𝑜𝑔 𝑥 − 4﷮𝑥 + 4﷯﷯+𝐶 = 1﷮8﷯𝑙𝑜𝑔 𝑥 − 4﷮𝑥 + 4﷯﷯+𝐶 Example 8 Find the following integrals: (ii) ﷮﷮ 𝑑𝑥﷮ ﷮2𝑥 − 𝑥﷮2﷯﷯﷯﷯ ﷮﷮ 𝑑𝑥﷮ ﷮2𝑥 − 𝑥﷮2﷯﷯﷯﷯ Adding and subtracting 1 in denominator = ﷮﷮ 𝑑𝑥﷮ ﷮− 𝑥﷮2﷯ + 2𝑥 + 1−1﷯﷯﷯ = ﷮﷮ 𝑑𝑥﷮ ﷮1 − 𝑥﷮2﷯ + 2𝑥 − 1﷯﷯﷯ = ﷮﷮ 𝑑𝑥﷮ ﷮1 − 𝑥﷮2﷯ − 2𝑥 + 1﷯﷯﷯﷯ = ﷮﷮ 𝑑𝑥﷮ ﷮1 − 𝑥 − 1﷯﷮2﷯﷯﷯﷯ = ﷮﷮ 𝑑𝑥﷮ ﷮ 1﷮2﷯ − 𝑥 − 1﷯﷮2﷯﷯﷯﷯ = sin﷮−1﷯﷮ 𝑥 − 1﷮1﷯+C﷯ = 𝒔𝒊𝒏﷮−𝟏﷯﷮ 𝒙−𝟏﷯+𝑪﷯

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