Ex 7.2, 36 - Class 12

Last updated at May 29, 2018 by Teachoo

Ex 7.2, 36 - Integrate (x + 1) (x + log x)2 / x - Ex 7.2

Transcript

Ex 7.2, 36 ((𝑥 + 1) (𝑥 + log⁡𝑥 )^2)/𝑥 Step 1: Let 𝑥+log⁡𝑥= 𝑡 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 1+1/𝑥= 𝑑𝑡/𝑑𝑥 (𝑥 + 1)/𝑥= 𝑑𝑡/𝑑𝑥 " " 𝑑𝑥 = ((𝑥 )/(𝑥 + 1))𝑑𝑡 Step 2: Integrating the function ∫1▒〖" " ((𝑥 + 1) (𝑥 + log⁡𝑥 )^2)/𝑥〗 . 𝑑𝑥 Putting the value of 𝑥−𝑙𝑜𝑔⁡𝑥=𝑡 & 𝑑𝑥=((𝑥 )/(𝑥 + 1))𝑑𝑡 = ∫1▒〖" " ((𝑥 + 1) (𝑡)^2)/𝑥〗 . (𝑥 )/((𝑥 + 1) ) . 𝑑𝑡 = ∫1▒〖" " 𝑡^2 〗. 𝑑𝑡" " = 𝑡^(2 + 1)/(2 + 1) +𝐶 = 𝑡^3/3 +𝐶 = 𝟏/𝟑 (𝒙+𝒍𝒐𝒈⁡𝒙 )^𝟑+𝑪

Ex 7.2

Ex 7.2, 36 Important You are here

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Chapter 7 Class 12 Integrals

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