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Example 3 - Chapter 7 Class 12 Integrals - Part 2

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Example 3 Find the following integrals: (ii) βˆ«β–’γ€–π‘π‘œπ‘ π‘’π‘ π‘₯(π‘π‘œπ‘ π‘’π‘ π‘₯+cot⁑π‘₯ ) γ€— 𝑑π‘₯ βˆ«β–’γ€–π‘π‘œπ‘ π‘’π‘ π‘₯(π‘π‘œπ‘ π‘’π‘ π‘₯+cot⁑π‘₯ ) γ€— 𝑑π‘₯ = βˆ«β–’(π‘π‘œπ‘ π‘’π‘ π‘₯+π‘π‘œπ‘ π‘’π‘ π‘₯ cot⁑π‘₯ ) 𝑑π‘₯ = βˆ«β–’γ€–π‘π‘œπ‘ π‘’π‘^2 π‘₯ 𝑑π‘₯γ€—+βˆ«β–’γ€–π‘π‘œπ‘ π‘’π‘ π‘₯ cot⁑π‘₯ γ€— 𝑑π‘₯ = βˆ’πœπ¨π­β‘π’™ βˆ’π’„π’π’”π’†π’„ 𝒙+π‘ͺ As ∫1β–’γ€–π‘π‘œπ‘ π‘’π‘^2 π‘₯γ€— 𝑑π‘₯=βˆ’cot⁑π‘₯+𝐢 ∫1β–’γ€–π‘π‘œπ‘ π‘’π‘ π‘₯ cot⁑π‘₯ 𝑑π‘₯γ€—=βˆ’π‘π‘œπ‘ π‘’π‘ π‘₯+𝐢

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