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Ex 7.6, 4 - Finding integration x log x - CBSE NCERT - Integration by partsSlide6.JPG


Transcript

Ex 7.6, 4 π‘₯ log⁑π‘₯ ∫1β–’γ€–π‘₯ log⁑π‘₯ γ€— 𝑑π‘₯ ∫1β–’γ€–π‘₯ log⁑π‘₯ γ€— 𝑑π‘₯=∫1β–’(log⁑π‘₯ )π‘₯ 𝑑π‘₯ =log⁑π‘₯ ∫1β–’π‘₯ 𝑑π‘₯βˆ’βˆ«1β–’(𝑑(log⁑π‘₯ )/𝑑π‘₯ ∫1β–’γ€–π‘₯.𝑑π‘₯γ€—)𝑑π‘₯ =log⁑π‘₯ (π‘₯^2/2)βˆ’βˆ«1β–’γ€–1/π‘₯ . π‘₯^2/2. 𝑑π‘₯γ€— =γ€–π‘₯^2/2 log〗⁑〖 π‘₯γ€—βˆ’1/2 ∫1β–’γ€–π‘₯. 𝑑π‘₯γ€— =γ€–π‘₯^2/2 log〗⁑π‘₯βˆ’1/2 . π‘₯^2/2 +𝐢 =〖𝒙^𝟐/𝟐 π’π’π’ˆγ€—β‘γ€– π’™γ€—βˆ’ 𝒙^𝟐/πŸ’ +π‘ͺ " "

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