Integration Full Chapter Explained - Integration Class 12 - Everything you need

Last updated at Dec. 20, 2019 by Teachoo
Transcript
Ex 7.2, 14 Integrate the function: 1/(๐ฅ(logโก๐ฅ )^๐ ) , ๐ฅ > 0 Step 1: Let logโก๐ฅ=๐ก Differentiating both sides ๐ค.๐.๐ก.๐ฅ 1/๐ฅ= ๐๐ก/๐๐ฅ ๐๐ฅ=๐ฅ . ๐๐ก Step 2: Integrating the function โซ1โใ" " 1/(๐ฅ(logโก๐ฅ )^๐ )ใ . ๐๐ฅ Putting ๐๐๐โก๐ฅ=๐ก & ๐๐ฅ=๐ฅ . ๐๐ก = โซ1โใ" " 1/(๐ฅ . ๐ก^๐ )ใ . ๐ฅ ๐๐ก = โซ1โใ" " 1/๐ก^๐ ใ . ๐๐ก = โซ1โใ" " ๐ก^(โ๐) ใ . ๐๐ก = ๐ก^(โ๐ + 1)/(โ๐ +1) +๐ถ = ๐ก^(1 โ ๐)/(1 โ ๐) +๐ถ Putting back t = log x = (๐๐๐โก๐ )^(๐ โ ๐)/(๐ โ ๐) +๐ช (Using โซ1โ๐ฅ^๐ . ๐๐ฅ=๐ฅ^(๐+1)/(๐ +1))
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