Ex 7.2, 35 - Integrate (1 + log x)2 / x - CBSE NCERT - Integration by substitution - lnx

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Ex 7.2, 35 1 + log﷮𝑥﷯﷯﷮2﷯﷮𝑥﷯ Step 1: Let 1+ log﷮𝑥﷯= 𝑡 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 0+ 1﷮𝑥﷯= 𝑑𝑡﷮𝑑𝑥﷯ 1﷮𝑥﷯= 𝑑𝑡﷮𝑑𝑥﷯ 𝑑𝑥 = 𝑥 . 𝑑𝑡 Step 2: Integrating the function ﷮﷮ 1 + log﷮𝑥﷯﷯﷮2﷯﷮𝑥﷯﷯. 𝑑𝑥 Putting 1− 𝑙𝑜𝑔﷮𝑥﷯=𝑡 & 𝑑𝑥=𝑥 . 𝑑𝑡 = ﷮﷮ 𝑡﷮2﷯﷮𝑥﷯ ﷯. 𝑥 . 𝑑𝑡 = ﷮﷮ 𝑡﷮2﷯﷯. 𝑑𝑡 = 𝑡﷮2 + 1﷯﷮2 + 1﷯ +𝐶 = 𝑡﷮3﷯﷮3﷯ +𝐶 = 𝟏﷮𝟑﷯ 𝟏+ 𝒍𝒐𝒈﷮𝒙﷯﷯﷮𝟑﷯+𝑪

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