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Misc 34 - Prove that dx/ x2 (x + 1) = 2/3 + log 2/3 - Definate Integration - By Partial Fraction

Misc 34 - Chapter 7 Class 12 Integrals - Part 2
Misc 34 - Chapter 7 Class 12 Integrals - Part 3

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Transcript

Misc 34 Prove that ﷐1﷮3﷮﷐𝑑𝑥﷮﷐𝑥﷮2﷯﷐𝑥 + 1﷯﷯= ﷐2﷮3﷯﷯+﷐log﷮﷐2﷮3﷯﷯ Solving L.H.S : ﷐1﷮3﷮﷐𝑑𝑥﷮﷐𝑥﷮2﷯﷐𝑥 + 1﷯﷯﷯ By partial fraction, ﷐1﷮﷐𝑥﷮2﷯(𝑥 + 1)﷯ = ﷐A﷮𝑥﷯+﷐B﷮﷐𝑥﷮2﷯﷯+﷐C﷮𝑥 + 1﷯ ﷐1﷮﷐𝑥﷮2﷯(𝑥 + 1)﷯ = ﷐ A 𝑥 ﷐𝑥 + 1﷯ + B ﷐𝑥 + 1﷯ + C﷐𝑥﷮2﷯﷮﷐𝑥﷮2﷯ (𝑥 + 1)﷯ ∴ 1 = Ax (x + 1) + B (x + 1) + C﷐𝑥﷮2﷯ Finding A,B,C

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.