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Example 2 - Chapter 7 Class 12 Integrals - Part 4

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Example 2 Find the following integrals: (iii) βˆ«β–’(π‘₯^(3/2)+2𝑒^π‘₯βˆ’1/π‘₯) 𝑑π‘₯ ∫1β–’(π‘₯^(3/2)+2𝑒^π‘₯βˆ’1/π‘₯) 𝑑π‘₯ =∫1β–’π‘₯^(3/2) 𝑑π‘₯+2∫1▒𝑒^π‘₯ 𝑑π‘₯βˆ’βˆ«1β–’1/π‘₯ 𝑑π‘₯ = π‘₯^(3/2 + 1)/(3/2 + 1) +2𝑒^π‘₯βˆ’log⁑〖 |π‘₯|γ€—+𝐢 = π‘₯^(5/2)/(5/2)+2𝑒^π‘₯βˆ’γ€–log 〗⁑|π‘₯|+𝐢 = γ€–πŸπ’™ γ€—^(πŸ“/𝟐)/πŸ“+πŸπ’†^π’™βˆ’γ€–π’π’π’ˆ 〗⁑|𝒙|+π‘ͺ As ∫1β–’π‘₯^𝑛 𝑑π‘₯=π‘₯^(𝑛 + 1)/(𝑛 + 1) +𝐢 ∫1▒𝑒^π‘₯ 𝑑π‘₯=𝑒^π‘₯ +𝐢 ∫1β–’1/π‘₯ 𝑑π‘₯=log⁑〖 |π‘₯|γ€— +𝐢

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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.