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For Finding Integration of lnx (log x),

we use Integration by Parts

 

We follow the following steps

  1. Write ∫ log x dx = ∫ (log x) . 1 dx
  2. Take first function as log x, second function as 1.
  3. Use integration by Parts and solve

Example 18 - Find integration log x (lnx) - Integration by parts

There are other formulas which are used to find Integral, refer Integral Table.

  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Transcript

Example 18 Find Intgeral of log x ln x ﷮﷮ log﷮𝑥﷯﷯ 𝑑𝑥 = ﷮﷮ log﷮𝑥﷯﷯﷯.1 𝑑𝑥 Using by parts I﷮𝑠𝑡﷯ function = f(x) = log﷮𝑥﷯ & II﷮𝑛𝑑﷯ function =g(x) = 1 ﷮﷮ log﷮𝑥﷯﷯﷯.1 𝑑𝑥= log﷮𝑥﷯ ﷮﷮1﷯. 𝑑𝑥− ﷮﷮ 𝑑 log﷮𝑥﷯﷯﷮𝑑𝑥﷯ ﷮﷮1 .𝑑𝑥﷯﷯﷯𝑑𝑥 = log﷮𝑥﷯﷯𝑥− ﷮﷮ 1﷮𝑥﷯﷯ . 𝑥 . 𝑑𝑥 = 𝑥 log﷮𝑥﷯− ﷮﷮1﷯. 𝑑𝑥 = 𝒙 𝒍𝒐𝒈﷮𝒙﷯−𝒙+𝑪

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