Misc 4 - Integrate 1 / x2 (x4 + 1)3/4 - Class 12 NCERT - Miscellaneous

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Misc 4 Integrate the function 1﷮ 𝑥﷮2﷯ 𝑥﷮4﷯ + 1﷯﷮ 3﷮4﷯﷯ ﷯ ﷮﷮ 1 𝑑𝑥﷮ 𝑥﷮2﷯ 𝑥﷮4﷯ + 1﷯﷮ 3﷮4﷯﷯ ﷯﷯ Taking 𝒙﷮𝟒﷯ common from denominator = ﷮﷮ 1 𝑑𝑥﷮ 𝑥﷮2 ﷯ (𝑥﷮4﷯)﷮ 3﷮4﷯﷯ 1 + 1﷮ 𝑥﷮4﷯﷯﷯﷮ 3﷮4﷯﷯﷯﷯ = ﷮﷮ 𝑑𝑥﷮ 𝑥﷮2﷯ (𝑥﷮3﷯) 1 + 1﷮ 𝑥﷮4﷯﷯﷯﷮ 3﷮4﷯﷯﷯﷯ = ﷮﷮ 𝑑𝑥﷮ 𝑥﷮5﷯ 1 + 1﷮ 𝑥﷮4﷯﷯﷯﷮ 3﷮4﷯﷯﷯﷯ Let t = 1 + 1﷮ 𝑥﷮4﷯﷯ 𝑑𝑡﷮𝑑𝑥﷯ = − 4﷮ 𝑥﷮5﷯﷯ − 𝑑𝑡﷮4﷯ = 𝑑𝑥﷮ 𝑥﷮5﷯﷯ Substituting value of x and dx = −1﷮4﷯ ﷮﷮ 𝑑𝑡﷮ 𝑡﷮ 3﷮4﷯﷯﷯﷯ = −1﷮4﷯ ﷮﷮ 𝑡﷮ −3﷮4﷯﷯﷯ 𝑑𝑡 = −1﷮4﷯ 𝑡﷮ −3﷮4﷯ + 1﷯﷮ −3﷮4﷯ + 1﷯﷯+ C = −1﷮4﷯ 𝑡﷮ 1﷮4﷯﷯﷮ 1﷮4﷯﷯﷯+ C = − 𝑡﷮ 1﷮4﷯﷯+ C = − 𝟏+ 𝟏﷮ 𝒙﷮𝟒﷯﷯﷯﷮ 𝟏﷮𝟒﷯﷯+ C

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.