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Example 11 - Find integral dx / (x + 1) (x + 2) - Integration by partial fraction - Type 1

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Example 11 Find ﷮﷮ 𝑑𝑥﷮ 𝑥 + 1﷯ 𝑥 + 2﷯﷯﷯ Using partial functions 1﷮(𝑥 + 1)(𝑥 + 2)﷯= A﷮𝑥 + 1﷯+ B﷮𝑥 + 2﷯ 1 = (x + 2)A + (x + 1)B 1 = x (A + B) + 2A + B Thus, B = −A = −1 Thus our equation becomes, ﷮﷮ 𝑑𝑥﷮ 𝑥 + 1﷯ (𝑥 + 2)﷯﷯= ﷮﷮ 1﷮𝑥 + 1﷯− 1﷮𝑥 + 2﷯﷯﷯𝑑𝑥 = log 𝑥 +1﷯− log 𝑥+2﷯+ C = log 𝒙 + 𝟏﷮𝒙 + 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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