# Ex 7.2, 7

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Ex 7.2, 7 (Method 1) Integrate the function: 𝑥 𝑥+2 𝑥 𝑥+2 Step 1: Let (𝑥+2)=𝑡 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 1+0 = 𝑑𝑡𝑑𝑥 1= 𝑑𝑡𝑑𝑥 𝑑𝑥=𝑑𝑡 Step 2: Integrating the function 𝑥 𝑥+2 .𝑑𝑥 putting the value of 𝑥+2 & 𝑑𝑥 . = 𝑥 𝑡 .𝑑𝑥 = 𝑥 𝑡 .𝑑𝑡 = 𝑡−2 𝑡 .𝑑𝑡 = 𝑡−2 𝑡 12 .𝑑𝑡 = 𝑡. 𝑡 12−2. 𝑡 12 .𝑑𝑡 = 𝑡 32−2. 𝑡 12 .𝑑𝑡 = 𝑡 32 .𝑑𝑡 − 2 𝑡 12 .𝑑𝑡 = 𝑡 32 + 1 32 + 1 − 2 . 𝑡 12 + 1 12 + 1 + 𝐶 = 𝑡 52 52 − 2 . 𝑡 32 32 + 𝐶 = 25 . 𝑡 52 − 2 . 23 𝑡 32 + 𝐶 = 25 . 𝑡 52 − 43 𝑡 32 + 𝐶 = 𝟐𝟓 . 𝒙+𝟐 𝟓𝟐 − 𝟒𝟑 𝒙+𝟐 𝟑𝟐 + 𝑪 Ex 7.2, 7 (Method 2) Integrate the function: 𝑥 𝑥+2 𝑥 𝑥+2 = 𝑥+2−2 𝑥+2 = 𝑥+2−2 𝑥+2 = 𝑥+2 𝑥+2−2 𝑥+2 = 𝑥+2 𝑥+2 12−2 𝑥+2 12 = 𝑥+2 12 +1−2 𝑥+2 12 = 𝑥+2 32−2 𝑥+2 12 ∴ 𝑥 𝑥+2 = 𝑥+2 32−2 𝑥+2 12 Step 2: Integrating the function 𝑥 𝑥+2 = 𝑥+2 32−2 𝑥+2 12. 𝑑𝑥 = 𝑥+2 32. 𝑑𝑥 − 2 𝑥+2 12. 𝑑𝑥 = 𝑥 + 2 32 + 1 32 + 1 − 2 𝑥+2 12 + 1 12 + 1 + 𝐶 = 𝑥 + 2 52 52 − 2 𝑥 + 2 32 32 + 𝐶 = 25 𝑥 + 2 52 − 2 . 2 3 𝑥 + 2 32 + 𝐶 = 𝟐𝟓 𝒙 + 𝟐 𝟓𝟐 − 𝟒𝟑 𝒙 + 𝟐 𝟑𝟐 + 𝑪

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.