Ex 7.1, 15 - Integrate root x (3x2 + 2x + 3) dx - Ex 7.1

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise

Transcript

Ex 7.1, 15 ﷮﷮ ﷮𝑥﷯(3 𝑥﷮2﷯+2𝑥+3)﷯𝑑𝑥 ﷮﷮ ﷮𝑥﷯(3 𝑥﷮2﷯+2𝑥+3)﷯𝑑𝑥 = ﷮﷮ 𝑥﷮ 1﷮2﷯﷯ 3 𝑥﷮2﷯+2𝑥+3﷯﷯𝑑𝑥 = ﷮﷮ 3 𝑥﷮ 1﷮2﷯﷯ . 𝑥﷮2﷯+2 𝑥﷮ 1﷮2﷯﷯ . 𝑥+3 𝑥﷮ 1﷮2﷯﷯﷯﷯𝑑𝑥 = ﷮﷮ 3 𝑥﷮ 1﷮2﷯ + 2﷯+2 𝑥﷮ 1﷮2﷯ + 1﷯+3 𝑥﷮ 1﷮2﷯﷯﷯﷯𝑑𝑥 = ﷮﷮ 3 𝑥﷮ 1 + 4﷮2﷯﷯+2 𝑥﷮ 1 + 2﷮2﷯﷯+3 𝑥﷮ 1﷮2﷯﷯﷯﷯𝑑𝑥 = ﷮﷮ 3 𝑥﷮ 5﷮2﷯﷯+2 𝑥﷮ 3﷮2﷯﷯+3 𝑥﷮ 1﷮2﷯﷯﷯﷯𝑑𝑥 =3 ﷮﷮ 𝑥﷮ 5﷮2﷯﷯﷯𝑑𝑥+2 ﷮﷮ 𝑥﷮ 3﷮2﷯﷯﷯𝑑𝑥+3 ﷮﷮ 𝑥﷮ 1﷮2﷯﷯﷯𝑑𝑥 = 3 . 𝑥﷮ 5﷮2﷯ + 1﷯﷮ 5﷮2﷯ + 1﷯ + 2 . 𝑥﷮ 3﷮2﷯ + 1﷯﷮ 3﷮2﷯ + 1﷯ + 3 𝑥﷮ 1﷮2﷯ + 1﷯﷮ 1﷮2﷯ + 1﷯+𝐶 = 3𝑥﷮ 7﷮2﷯﷯﷮ 7﷮2﷯﷯ + 2 𝑥﷮ 5﷮2﷯ ﷯﷮ 5﷮2﷯﷯ + 3 𝑥﷮ 3﷮2﷯﷯﷮ 3﷮2﷯﷯ +𝐶 =3× 2 𝑥﷮ 7﷮2﷯﷯﷮7﷯ +2× 2 𝑥﷮ 5﷮2﷯ ﷯﷮5﷯ +3× 2 𝑥﷮ 3﷮2﷯﷯﷮3﷯ +𝐶 = 𝟔 𝒙﷮ 𝟕﷮𝟐﷯﷯﷮𝟕﷯ + 𝟒 𝒙﷮ 𝟓﷮𝟐﷯ ﷯﷮𝟓﷯ + 𝟐𝒙﷮ 𝟑﷮𝟐﷯﷯+𝑪

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