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Ex 7.2, 1 - Integrate 2x/ 1 + x2 - Chapter 7 Class 12 - Ex 7.2

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Ex 7.2, 1 Integrate the function: 2𝑥﷮1+𝑥2﷯ Let 1 + 𝑥2 = 𝑡 Differentiate 𝑤.𝑟.𝑡.𝑥 2𝑥= 𝑑𝑡﷮𝑑𝑥﷯ 𝑑𝑥= 𝑑𝑡﷮2𝑥﷯ Thus, our equation becomes ﷮﷮ 2𝑥﷮1 + 𝑥2﷯﷯ 𝑑𝑥 = ﷮﷮ 2𝑥﷮𝑡﷯﷯ . 𝑑𝑡﷮2𝑥﷯ = ﷮﷮ 𝑑𝑡﷮𝑡﷯﷯ = log 𝑡﷯+𝐶 Putting 𝑡 = 1 + 𝑥﷮2﷯ = log 1+ 𝑥﷮2﷯﷯+𝐶 = log 1+ 𝑥﷮2﷯﷯+𝐶

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