Ex 7.2, 3 Integrate the function: 1/(𝑥 + 𝑥 log⁡𝑥 ) 1/(𝑥 + 𝑥 log⁡𝑥 )=1/𝑥(1 + log⁡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 function ∫1▒1/(𝑥 + 𝑥 log⁡𝑥 ) .𝑑𝑥 =∫1▒1/(𝑥 (1 + log⁡𝑥 ) ) .𝑑𝑥" " Putting 1+log⁡𝑥 & 𝑑𝑥=𝑥 𝑑𝑡 = ∫1▒1/(𝑥(𝑡)) 𝑑𝑡.𝑥 = ∫1▒1/𝑡 𝑑𝑡 = 𝑙𝑜𝑔|𝑡|+𝐶 Putting back 𝑡 =1+𝑙𝑜𝑔⁡𝑥 = 𝒍𝒐𝒈|𝟏+𝐥𝐨𝐠⁡𝒙 |+𝑪 (𝑈𝑠𝑖𝑛𝑔∫1▒〖1/𝑥 𝑑𝑥〗=log⁡|𝑥|+𝐶)

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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