Ex 7.2, 14 - Integrate: 1 / x(log x)m - Chapter 7 CBSE - Integration by substitution - lnx

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  1. Chapter 7 Class 12 Integrals
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Ex 7.2, 14 Integrate the function: 1﷮𝑥 log﷮𝑥﷯﷯﷮𝑚﷯﷯ , 𝑥 > 0 Step 1: Let log﷮𝑥﷯=𝑡 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 1﷮𝑥﷯= 𝑑𝑡﷮𝑑𝑥﷯ 𝑑𝑥=𝑥 . 𝑑𝑡 Step 2: Integrating the function ﷮﷮ 1﷮𝑥 log﷮𝑥﷯﷯﷮𝑚﷯﷯﷯ . 𝑑𝑥 putting 𝑙𝑜𝑔﷮𝑥﷯=𝑡 & 𝑑𝑥=𝑥 . 𝑑𝑡 = ﷮﷮ 1﷮𝑥 . 𝑡﷮𝑚﷯﷯﷯ . 𝑥 𝑑𝑡 = ﷮﷮ 1﷮ 𝑡﷮𝑚﷯﷯﷯ . 𝑑𝑡 = ﷮﷮ 𝑡﷮−𝑚﷯﷯ . 𝑑𝑡 = 𝑡﷮− 𝑚 + 1﷯﷮−𝑚 +1﷯ +𝐶 = 𝑡﷮1 − 𝑚﷯﷮1 −𝑚﷯ +𝐶 = 𝒍𝒐𝒈﷮𝒙﷯﷯﷮𝟏 − 𝒎﷯﷮𝟏 − 𝒎﷯ +𝑪

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