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Ex 7.7, 7 - Integrate root 1 + 3x - x2 - Chapter 7 CBSE - Integration by specific formulaes - Formula 8

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Ex7.7, 7 ﷮1+3𝑥−𝑥2﷯ ﷮﷮ ﷮1+3𝑥− 𝑥﷮2﷯﷯ 𝑑𝑥﷯ = ﷮﷮ ﷮1− −3𝑥+ 𝑥﷮2﷯﷯﷯ 𝑑𝑥﷯ = ﷮﷮ ﷮1− 𝑥﷮2﷯−3𝑥﷯﷯ 𝑑𝑥﷯ = ﷮﷮ ﷮1− 𝑥﷮2﷯−2 3﷮2﷯﷯ 𝑥﷯﷯﷯ 𝑑𝑥﷯ = ﷮﷮ ﷮1− 𝑥﷮2﷯−2 3﷮2﷯﷯ 𝑥﷯+ 3﷮2﷯﷯﷮2﷯− 3﷮2﷯﷯﷮2﷯﷯﷯ 𝑑𝑥﷯ = ﷮﷮ ﷮1− 𝑥− 3﷮2﷯﷯﷮2﷯− 9﷮4﷯﷯﷯ 𝑑𝑥﷯ = ﷮﷮ ﷮1− 𝑥− 3﷮2﷯﷯﷮2﷯+ 9﷮4﷯﷯ 𝑑𝑥﷯ = ﷮﷮ ﷮1+ 9﷮4﷯− 𝑥− 3﷮2﷯﷯﷮2﷯﷯ 𝑑𝑥﷯ = ﷮﷮ ﷮ 13﷮4﷯− 𝑥− 3﷮2﷯﷯﷮2﷯﷯ 𝑑𝑥﷯ = ﷮﷮ ﷮ ﷮13﷯﷮2﷯﷯﷮2﷯− 𝑥− 3﷮2﷯﷯﷮2﷯﷯ 𝑑𝑥﷯ = 𝑥 − 3﷮2﷯﷮2﷯ ﷮ ﷮13﷯﷮2﷯﷯﷮2﷯− 𝑥− 3﷮2﷯﷯﷮2﷯﷯+ ﷮13﷯﷮2﷯﷯﷮2﷯﷮2﷯𝑠𝑖 𝑛﷮−1﷯ 𝑥 − 3﷮2﷯﷯﷮ ﷮13﷯﷮2﷯﷯+𝐶 = 2𝑥 − 3﷮2﷯﷮2﷯ ﷮ 13﷮4﷯− 𝑥− 3﷮2﷯﷯﷮2﷯﷯+ 13﷮4﷯﷮2﷯𝑠𝑖 𝑛﷮−1﷯ 2𝑥 − 3﷮2﷯﷯﷮ ﷮13﷯﷮2﷯﷯+𝐶 = 2𝑥 − 3﷮4﷯ ﷮ 13﷮4﷯− 𝑥− 3﷮2﷯﷯﷮2﷯﷯+ 13﷮8﷯𝑠𝑖 𝑛﷮−1﷯ 2𝑥 − 3﷮ ﷮13﷯﷯+𝐶 = 2𝑥 − 3﷮4﷯ ﷮ 13﷮4﷯− 𝑥﷮2﷯+ 9﷮4﷯−2 𝑥﷯ 3﷮2﷯﷯﷯﷯+ 13﷮8﷯𝑠𝑖 𝑛﷮−1﷯ 2𝑥 − 3﷮ ﷮13﷯﷯+𝐶 = 2𝑥 − 3﷮4﷯ ﷮ 13﷮4﷯− 𝑥﷮2﷯− 9﷮4﷯+3𝑥﷯+ 13﷮8﷯𝑠𝑖 𝑛﷮−1﷯ 2𝑥 − 3﷮ ﷮13﷯﷯+𝐶 = 2𝑥 − 3﷮4﷯ ﷮ 13﷮4﷯− 9﷮4﷯+3𝑥− 𝑥﷮2﷯﷯+ 13﷮8﷯𝑠𝑖 𝑛﷮−1﷯ 2𝑥 − 3﷮ ﷮13﷯﷯+𝐶 = 𝟐𝒙 − 𝟑﷮𝟒﷯ ﷮𝟏+𝟑𝒙− 𝒙﷮𝟐﷯﷯+ 𝟏𝟑﷮𝟖﷯𝒔𝒊 𝒏﷮−𝟏﷯ 𝟐𝒙 − 𝟑﷮ ﷮𝟏𝟑﷯﷯﷯+𝑪

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