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Misc 2 - Integrate 1/root x+a + root x+b - Class 12 - Miscellaneous

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Misc 2 Integrate the function 1﷮ ﷮𝑥 + 𝑎﷯ + ﷮𝑥 +𝑏﷯ ﷯ ﷮﷮ 1﷮ ﷮𝑥 + 𝑎﷯ + ﷮𝑥 + 𝑏﷯ ﷯ 𝑑𝑥﷯ Rationalising = ﷮﷮ 1﷮ ﷮𝑥 + 𝑎﷯ + ﷮𝑥 + 𝑏﷯ ﷯ × ﷮𝑥 + 𝑎﷯ − ﷮𝑥 + 𝑏﷯﷮ ﷮𝑥 + 𝑎﷯ − ﷮𝑥 + 𝑏﷯ ﷯﷯ 𝑑𝑥﷯ = ﷮﷮ ﷮𝑥 + 𝑎﷯ − ﷮𝑥 + 𝑏﷯﷮ ﷮𝑥 + 𝑎﷯ + ﷮𝑥 + 𝑏﷯ ﷯ ﷮𝑥 + 𝑎﷯ − ﷮𝑥 + 𝑏﷯ ﷯ ﷯𝑑𝑥﷯ = ﷮﷮ ﷮𝑥 + 𝑎﷯ − ﷮𝑥 + 𝑏﷯﷮ ﷮𝑥 + 𝑎﷯ ﷯﷮2﷯ − ﷮𝑥 + 𝑏﷯ ﷯﷮2﷯ ﷯𝑑𝑥﷯ = ﷮﷮ ﷮𝑥 + 𝑎﷯ − ﷮𝑥 + 𝑏﷯﷮𝑥 + 𝑎 − 𝑥 + 𝑏﷯﷯𝑑𝑥﷯ = ﷮﷮ ﷮𝑥 + 𝑎﷯ − ﷮𝑥 + 𝑏﷯﷮𝑎 − 𝑏﷯𝑑𝑥﷯ = 1﷮𝑎 − 𝑏﷯ ﷮﷮ ﷮𝑥+𝑎﷯ − ﷮𝑥+𝑏﷯ ﷯﷯𝑑𝑥 = 1﷮𝑎 − 𝑏﷯ ﷮﷮ 𝑥+𝑎﷯﷮ 1﷮2﷯﷯ − 𝑥+𝑎﷯﷮ 1﷮2﷯﷯﷯﷯𝑑𝑥 = 1﷮𝑎 − 𝑏﷯ ﷮﷮ 𝑥+𝑎﷯﷮ 1﷮2﷯﷯﷯𝑑𝑥− ﷮﷮ 𝑥+𝑎﷯﷮ 1﷮2﷯﷯﷯𝑑𝑥﷯ = 1﷮𝑎 − 𝑏﷯ 𝑥 + 𝑎﷯﷮ 1﷮2﷯ + 1﷯﷮ 1﷮2﷯ + 1﷯ − 𝑥 + 𝑏﷯﷮ 1﷮2﷯ + 1﷯﷮ 1﷮2﷯ + 1﷯ ﷯ + 𝐶 = 1﷮𝑎 − 𝑏﷯ 𝑥 + 𝑎﷯﷮ 3﷮2﷯﷯﷮ 3﷮2﷯﷯ − 𝑥 + 𝑏﷯﷮ 3﷮2﷯﷯﷮ 3﷮2﷯﷯﷯ + 𝐶 = 1﷮𝑎 − 𝑏﷯ 2 𝑥 + 𝑎﷯﷮ 3﷮2﷯﷯﷮3﷯ − 2 𝑥 + 𝑏﷯﷮ 3﷮2﷯﷯﷮3﷯﷯ + 𝐶 = 𝟐﷮𝟑 𝒂 − 𝒃﷯﷯ 𝒙+𝒂﷯﷮ 𝟑﷮𝟐﷯﷯− 𝒙+𝒃﷯﷮ 𝟑﷮𝟐﷯﷯﷯ + 𝑪

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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