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Ex 7.2, 15 - Integrate x/(9 - 4x2) - Chapter 7 NCERT - Integration by substitution - x^n

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Ex 7.2, 15 Integrate the function: 𝑥﷮9 − 4𝑥2﷯ Step 1: Let 9 – 4𝑥2 = 𝑡 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 0−4.2 𝑥﷮2−1﷯= 𝑑𝑡﷮𝑑𝑥﷯ −8𝑥.𝑑𝑥=𝑑𝑡 𝑑𝑥 = 𝑑𝑡﷮−8𝑥﷯ Step 2: Integrating the function ﷮﷮ 𝑥﷮9 − 4𝑥2﷯﷯ . 𝑑𝑥 Putting 9 − 4𝑥2=𝑡 & 𝑑𝑥= 𝑑𝑡﷮−8𝑥﷯ = ﷮﷮ 𝑥﷮𝑡﷯﷯ . 𝑑𝑡﷮−8𝑥﷯ = − 1﷮8﷯ ﷮﷮ 1﷮𝑡﷯﷯ . 𝑑𝑡 = − 1﷮8﷯ log ﷮ 𝑡﷯﷯+𝐶 = − 𝟏﷮𝟖﷯ 𝐥𝐨𝐠 ﷮ 𝟗 − 𝟒𝒙𝟐﷯﷯+𝑪

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