Example 38 - Evaluate integral (x4 - x)1/4 / x5 dx - Examples

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Example 38 Evaluate ﷮﷮ 𝑥﷮4﷯ −𝑥﷯﷮ 1﷮4﷯﷯﷮ 𝑥﷮5﷯﷯﷯ 𝑑𝑥 ﷮﷮ 𝑥﷮4﷯ − 𝑥﷯﷮ 1﷮4﷯﷯﷮ 𝑥﷮5﷯﷯﷯ 𝑑𝑥 Taking 𝑥﷮4﷯ common from numerator = ﷮﷮ 𝑥﷮4﷯﷯﷮ 1﷮4﷯﷯ 1 − 𝑥﷮ 𝑥﷮4﷯﷯﷯﷮ 1﷮4﷯﷯﷮ 𝑥﷮5﷯﷯﷯ 𝑑𝑥 = ﷮﷮ 𝑥 1 − 1﷮ 𝑥﷮3﷯﷯﷯﷮ 1﷮4﷯﷯﷮ 𝑥﷮5﷯﷯﷯ 𝑑𝑥 = ﷮﷮ 1 − 1﷮ 𝑥﷮3﷯﷯﷯﷮ 1﷮4﷯﷯﷮ 𝑥﷮4﷯﷯﷯ 𝑑𝑥 Let t = 1 − 1﷮ 𝑥﷮3﷯﷯ 𝑑𝑡﷮𝑑𝑥﷯= 3﷮ 𝑥﷮4﷯﷯ Substituting values, = ﷮﷮ 𝑡 ﷮ 1﷮4﷯﷯﷮3﷯﷯ 𝑑𝑡 = 1﷮3﷯ 𝑡﷮ 1﷮4 ﷯ + 1﷯﷯﷮ 1﷮4﷯ +1﷯﷯+ C = 1﷮3﷯ 𝑡﷮ 5﷮4﷯﷯ ﷮ 5﷮4﷯﷯﷯+ C = 4﷮15﷯ 𝑡 ﷮ 5﷮4﷯﷯+ C = 𝟒﷮𝟏𝟓﷯ 𝟏− 𝟏﷮ 𝒙﷮𝟑﷯﷯﷯﷮ 𝟓﷮𝟒﷯﷯+ C

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