Ex 7.6, 17 - Integrate x ex (1 + x)2 - Chapter 7 Class 12 - Ex 7.6

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  1. Chapter 7 Class 12 Integrals
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Ex7.6, 17 𝑥𝑒𝑥﷮ 1 + 𝑥﷯2﷯ ﷮﷮ 𝑥 𝑒﷮𝑥﷯﷮ 1 + 𝑥﷯﷮2﷯﷯ 𝑑𝑥﷯ = ﷮﷮𝑒𝑥 𝑥﷮ 1 + 𝑥﷯﷮2﷯﷯ 𝑑𝑥﷯ = ﷮﷮𝑒𝑥 𝑥 + 1 − 1﷮ 1 + 𝑥﷯﷮2﷯﷯﷯ 𝑑𝑥﷯ = ﷮﷮𝑒𝑥 1 + 𝑥﷮ 1 + 𝑥﷯﷮2﷯﷯ − 1﷮ 1 + 𝑥﷯﷮2﷯﷯﷯ 𝑑𝑥﷯ = ﷮﷮𝑒𝑥 1﷮ 1 + 𝑥﷯﷯ − 1﷮ 1 + 𝑥﷯﷮2﷯﷯﷯ 𝑑𝑥﷯ Putting, 𝑓 𝑥﷯= 1﷮1 + 𝑥﷯ ∴ 𝑓﷮′﷯ 𝑥﷯= − 1﷮ 1 + 𝑥﷯﷮2﷯﷯ ﷮﷮𝑒𝑥 1﷮1 + 𝑥﷯ − 1﷮ 1 + 𝑥﷯﷮2﷯﷯﷯ 𝑑𝑥﷯ = 𝒆𝒙﷮𝟏 + 𝒙﷯+𝑪

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