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Chapter 7 Class 12 Integrals
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Ex 7.6, 5 - Integrate x log 2x - Chapter 7 Class 12 - Integration by parts

Ex 7.6, 5 - Chapter 7 Class 12 Integrals - Part 2

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Ex 7.6, 5 π‘₯ log⁑2π‘₯ Integrating the function 𝑀.π‘Ÿ.𝑑.π‘₯ ∫1β–’γ€–π‘₯ log⁑2π‘₯ γ€— 𝑑π‘₯ Hence, we take First function :- 𝑓(π‘₯)=log⁑(2π‘₯) Second function :- g(π‘₯)=π‘₯ ∫1β–’γ€–π‘₯ log⁑π‘₯ γ€— 𝑑π‘₯=∫1β–’(log⁑π‘₯ )π‘₯ 𝑑π‘₯ =log⁑(2π‘₯) ∫1β–’π‘₯ 𝑑π‘₯βˆ’βˆ«1β–’(𝑑(log⁑2π‘₯ )/𝑑π‘₯ ∫1β–’γ€–π‘₯.𝑑π‘₯γ€—)𝑑π‘₯ =log⁑(2π‘₯) (π‘₯^2/2)βˆ’βˆ«1β–’γ€–1/2π‘₯ . 2 .π‘₯^2/2. 𝑑π‘₯γ€— =γ€–π‘₯^2/2 log〗⁑(2π‘₯)βˆ’βˆ«1β–’γ€–π‘₯/2. 𝑑π‘₯γ€— =γ€–π‘₯^2/2 log〗⁑(2π‘₯)βˆ’1/2 ∫1β–’γ€–π‘₯ 𝑑π‘₯γ€— =γ€–π‘₯^2/2 log〗⁑(π‘₯)βˆ’ 1/2 (π‘₯^2/2)+𝐢 =γ€–π‘₯^2/2 log〗⁑(2π‘₯)βˆ’ π‘₯^2/4 +𝐢

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