Example 2 - Find integrals (i) x3 - 1 / x2 dx - Examples

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Example 2 Find the following integrals: (i) ﷮﷮ 𝑥﷮3﷯ − 1﷮ 𝑥﷮2﷯﷯﷯ 𝑑𝑥 ﷮﷮ 𝑥﷮3﷯−1﷯﷮ 𝑥﷮2﷯﷯.𝑑𝑥﷯ = ﷮﷮ 𝑥﷮3﷯﷮ 𝑥﷮2﷯﷯− 1﷮ 𝑥﷮2﷯﷯﷯𝑑𝑥﷯ = ﷮﷮ 𝑥− 1﷮ 𝑥﷮2﷯﷯﷯.𝑑𝑥﷯ = ﷮﷮𝑥 𝑑𝑥− ﷮﷮ 1﷮ 𝑥﷮2﷯﷯ 𝑑𝑥﷯﷯ = ﷮﷮ 𝑥﷮1﷯ 𝑑𝑥− ﷮﷮ 𝑥﷮−2﷯. 𝑑𝑥﷯﷯ = 𝑥﷮1+1﷯﷮1+1﷯﷯+𝐶1﷯− 𝑥﷮−2+1﷯﷮−2+1﷯﷯+𝐶2﷯ = 𝑥﷮2﷯﷮2﷯+𝐶1﷯− 𝑥﷮−1﷯﷮−1﷯+𝐶2﷯ = 𝑥﷮2﷯﷮2﷯+𝐶1− −1﷮𝑥﷯+𝐶2﷯ = 𝑥﷮2﷯﷮2﷯+𝐶1+ 1﷮𝑥﷯−𝐶2 = 𝑥﷮2﷯﷮2﷯+ 1﷮𝑥﷯ +𝐶1− 𝐶2 = 𝒙﷮𝟐﷯﷮𝟐﷯+ 𝟏﷮𝒙﷯ +𝑪 Example 2 Find the following integrals: (ii) ﷮﷮ 𝑥﷮ 2﷮3﷯﷯+1﷯﷯ 𝑑𝑥 ﷮﷮ 𝑥﷮ 2﷮3﷯﷯+1﷯﷯𝑑𝑥 = ﷮﷮ 𝑥﷮ 2﷮3﷯﷯+ 𝑥﷮0﷯﷯𝑑𝑥﷯ = ﷮﷮ 𝑥﷮ 2﷮3﷯﷯﷯𝑑𝑥+ ﷮﷮ 𝑥﷮0﷯﷯𝑑𝑥 = 𝑥﷮ 2﷮3﷯ + 1﷯﷮ 2﷮3﷯ + 1﷯+ 𝑥﷮0 + 1﷯﷮0 + 1﷯+𝐶 = 𝑥﷮ 5﷮3﷯﷯﷮ 5﷮3﷯﷯+𝑥+𝐶 = 𝟑𝒙﷮ 𝟓﷮𝟑﷯﷯﷮𝟓﷯+𝒙+𝑪 Example 2 Find the following integrals: (iii) ﷮﷮ 𝑥﷮ 3﷮2﷯﷯+2 𝑒﷮𝑥﷯− 1﷮𝑥﷯﷯﷯ 𝑑𝑥 ﷮﷮ 𝑥﷮ 3﷮2﷯﷯+2 𝑒﷮𝑥﷯− 1﷮𝑥﷯﷯﷯𝑑𝑥 = ﷮﷮ 𝑥﷮ 2﷮3﷯﷯﷯𝑑𝑥+2 ﷮﷮ 𝑒﷮𝑥﷯﷯𝑑𝑥− ﷮﷮ 1﷮𝑥﷯﷯𝑑𝑥 = 𝑥﷮ 3﷮2﷯ + 1﷯﷮ 3﷮2﷯ + 1﷯ +2 𝑒﷮𝑥﷯− log﷮ 𝑥﷯﷯+𝐶 = 𝑥﷮ 5﷮2﷯﷯﷮ 5﷮2﷯﷯+2 𝑒﷮𝑥﷯− log﷮ 𝑥﷯﷯+𝐶 = 𝟐𝒙 ﷮ 𝟓﷮𝟐﷯﷯﷮𝟓﷯+𝟐 𝒆﷮𝒙﷯− 𝒍𝒐𝒈﷮ 𝒙﷯﷯+𝑪

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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