Ex 7.2, 2 - Integrate:  (log x)2 / x - Chapter 7 NCERT - Integration by substitution - x^n

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  1. Chapter 7 Class 12 Integrals
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Ex 7.2, 2 Integrate the function: (log⁑π‘₯ )^2/π‘₯ Step 1: Let log π‘₯= 𝑑 Differentiate 𝑀.π‘Ÿ.𝑑.π‘₯ 𝑑𝑑/𝑑π‘₯= 1/π‘₯ 𝑑𝑑.π‘₯=𝑑π‘₯ 𝑑π‘₯=𝑑𝑑.π‘₯ Step 2: Integrating function ∫1β–’(log⁑π‘₯ )^2/π‘₯ 𝑑π‘₯ Putting (π‘™π‘œπ‘”β‘π‘₯ )^2=𝑑=π‘₯ 𝑑𝑑 = ∫1▒𝑑^2/π‘₯ 𝑑𝑑.π‘₯ = ∫1▒〖𝑑^2 𝑑𝑑〗 = 𝑑^(2+1)/(2+1)+𝐢 = 𝑑^3/3+𝐢 Putting 𝑑=log⁑|π‘₯| =𝟏/πŸ‘ (π’π’π’ˆβ‘|𝒙| )^πŸ‘+π‘ͺ

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