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

Last updated at Dec. 20, 2019 by Teachoo
Transcript
Ex 7.2, 3 Integrate the function: 1/(๐ฅ + ๐ฅ logโก๐ฅ ) 1/(๐ฅ + ๐ฅ logโก๐ฅ )=1/๐ฅ(1 + logโก๐ฅ ) Step 1: Let 1+logโก๐ฅ=๐ก Differentiating both sides ๐ค.๐.๐ก.๐ฅ 0 + 1/๐ฅ=๐๐ก/๐๐ฅ 1/๐ฅ=๐๐ก/๐๐ฅ ๐๐ฅ=๐ฅ ๐๐ก Step 2: Integrating function โซ1โ1/(๐ฅ + ๐ฅ logโก๐ฅ ) .๐๐ฅ =โซ1โ1/(๐ฅ (1 + logโก๐ฅ ) ) .๐๐ฅ" " Putting 1+logโก๐ฅ & ๐๐ฅ=๐ฅ ๐๐ก = โซ1โ1/(๐ฅ(๐ก)) ๐๐ก.๐ฅ = โซ1โ1/๐ก ๐๐ก = ๐๐๐|๐ก|+๐ถ Putting back ๐ก =1+๐๐๐โก๐ฅ = ๐๐๐|๐+๐ฅ๐จ๐ โก๐ |+๐ช (๐๐ ๐๐๐โซ1โใ1/๐ฅ ๐๐ฅใ=logโก|๐ฅ|+๐ถ)
Integration by substitution - lnx
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