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Find ∫ 𝑒 π‘₯ (1 βˆ’ cot π‘₯ + π‘π‘œπ‘ π‘’π‘ 2 π‘₯) 𝑑

Find ∫ e^x (1 - cot x + cosec^2 x) dx - Integration [Video] - Teachoo

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Question 7 (Choice 1) Find ∫ 𝑒π‘₯ (1 βˆ’ cot π‘₯ + π‘π‘œπ‘ π‘’π‘2π‘₯) 𝑑x ∫ 𝑒π‘₯ ( [1 βˆ’ cot π‘₯] + π‘π‘œπ‘ π‘’π‘2π‘₯) 𝑑x It is of the form ∫1▒〖𝒆^𝒙 [𝒇(𝒙)+𝒇^β€² (𝒙)] γ€— 𝒅𝒙=𝒆^𝒙 𝒇(𝒙)+π‘ͺ Where 𝑓(π‘₯)=1βˆ’cot⁑π‘₯ 𝑓^β€² (π‘₯)=0βˆ’(βˆ’π‘π‘œπ‘ π‘’π‘^2 π‘₯)=π‘π‘œπ‘ π‘’π‘^2 π‘₯ So, our equation becomes ∫ 𝑒π‘₯ ( [1 βˆ’ cot π‘₯] + π‘π‘œπ‘ π‘’π‘2π‘₯) 𝑑x" " = 𝒆^𝒙 (πŸβˆ’π’„π’π’• 𝒙) +π‘ͺ

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.