**Example 2**

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

Transcript

Example 2 Find the following integrals: (i) 𝑥3 − 1 𝑥2 𝑑𝑥 𝑥3−1 𝑥2.𝑑𝑥 = 𝑥3 𝑥2− 1 𝑥2𝑑𝑥 = 𝑥− 1 𝑥2.𝑑𝑥 = 𝑥 𝑑𝑥− 1 𝑥2 𝑑𝑥 = 𝑥1 𝑑𝑥− 𝑥−2. 𝑑𝑥 = 𝑥1+11+1+𝐶1− 𝑥−2+1−2+1+𝐶2 = 𝑥22+𝐶1− 𝑥−1−1+𝐶2 = 𝑥22+𝐶1− −1𝑥+𝐶2 = 𝑥22+𝐶1+ 1𝑥−𝐶2 = 𝑥22+ 1𝑥 +𝐶1− 𝐶2 = 𝒙𝟐𝟐+ 𝟏𝒙 +𝑪 Example 2 Find the following integrals: (ii) 𝑥 23+1 𝑑𝑥 𝑥 23+1𝑑𝑥 = 𝑥 23+ 𝑥0𝑑𝑥 = 𝑥 23𝑑𝑥+ 𝑥0𝑑𝑥 = 𝑥 23 + 1 23 + 1+ 𝑥0 + 10 + 1+𝐶 = 𝑥 53 53+𝑥+𝐶 = 𝟑𝒙 𝟓𝟑𝟓+𝒙+𝑪 Example 2 Find the following integrals: (iii) 𝑥 32+2 𝑒𝑥− 1𝑥 𝑑𝑥 𝑥 32+2 𝑒𝑥− 1𝑥𝑑𝑥 = 𝑥 23𝑑𝑥+2 𝑒𝑥𝑑𝑥− 1𝑥𝑑𝑥 = 𝑥 32 + 1 32 + 1 +2 𝑒𝑥− log 𝑥+𝐶 = 𝑥 52 52+2 𝑒𝑥− log 𝑥+𝐶 = 𝟐𝒙 𝟓𝟐𝟓+𝟐 𝒆𝒙− 𝒍𝒐𝒈 𝒙+𝑪

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About the Author

Davneet Singh

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.