Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class
Integration by specific formulaes - Formula 7
Integration by specific formulaes - Formula 7
Last updated at May 29, 2023 by Teachoo
Example 23 Find 𝑥2+2𝑥+5 𝑑𝑥 𝑥2+2𝑥+5 𝑑𝑥 = 𝑥2+2𝑥+1+4 𝑑𝑥 = (𝑥+1)2+4 𝑑𝑥 Let y = x + 1 𝑑𝑦 𝑑𝑥=1 dy = dx Substituting = 𝑦2+4 𝑑𝑦 = 𝑦2+(2)2 𝑑𝑦 = 𝑦2 𝑦2+4+ 42 log𝑦+𝑦2+4+ C = 𝑦2𝑦2+4+2 𝑙𝑜𝑔𝑦+𝑦2+4+ C Putting value of y = x + 1 = 𝑥 + 12 (𝑥+1)2 + 4+2 𝑙𝑜𝑔𝑥+1+(𝑥+1)2 + 4+ C = 𝑥 + 12𝑥2+1+2𝑥+ 4+2 𝑙𝑜𝑔𝑥+1+𝑥2+1+2𝑥+ 4+ C = 𝟏𝟐 (x + 1) 𝒙𝟐 𝟐𝒙+𝟓+𝟐𝐥𝐨𝐠𝒙+𝟏+𝒙𝟐+𝟐𝒙+𝟓+𝐂