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

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  1. Chapter 7 Class 12 Integrals
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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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