Ex 7.2, 18 – Chapter 7 Class 12 Integrals

Last updated at May 29, 2023 by Teachoo

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Last updated at May 29, 2023 by Teachoo

Ex 7.2, 18 𝑒 tan−1 𝑥1 + 𝑥2 Step 1: Let tan−1 𝑥 = 𝑡 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 11 + 𝑥2= 𝑑𝑡𝑑𝑥 𝑑𝑥 = 1 + 𝑥2𝑑𝑡 Step 2: Integrating the function 𝑒 tan−1 𝑥1 + 𝑥2 . 𝑑𝑥 putting 𝑡𝑎𝑛−1 𝑥=𝑡 & 𝑑𝑥= 1 + 𝑥2𝑑𝑡 = 𝑒𝑡1 + 𝑥2 . 1 + 𝑥2𝑑𝑡 = 𝑒𝑡 . 𝑑𝑡 = 𝑒𝑡+𝐶 = 𝒆 𝒕𝒂𝒏−𝟏 𝒙+𝑪