Integration by substitution - Trignometric - Inverse

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Chapter 7 Class 12 Integrals
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Ex 7.2, 18 - Chapter 7 Class 12 Integrals

Last updated at Dec. 16, 2024 by

Ex 7.2, 18 - Integrate e tan-1 x / 1 + x2 - NCERT - Integration by substitution - Trignometric - Inverse

Ex 7.2, 18 - Chapter 7 Class 12 Integrals - Part 2

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Ex 7.2, 18 𝑒﷮ tan﷮−1﷯ 𝑥﷯﷮1 + 𝑥2﷯ Step 1: Let tan﷮−1﷯ 𝑥 = 𝑡 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 1﷮1 + 𝑥2﷯= 𝑑𝑡﷮𝑑𝑥﷯ 𝑑𝑥 = 1 + 𝑥2﷯𝑑𝑡 Step 2: Integrating the function ﷮﷮ 𝑒﷮ tan﷮−1﷯ 𝑥﷯﷮1 + 𝑥2﷯ ﷯. 𝑑𝑥 putting 𝑡𝑎𝑛﷮−1﷯ 𝑥=𝑡 & 𝑑𝑥= 1 + 𝑥2﷯𝑑𝑡 = ﷮﷮ 𝑒﷮𝑡﷯﷮1 + 𝑥2﷯﷯ . 1 + 𝑥2﷯𝑑𝑡 = ﷮﷮ 𝑒﷮𝑡﷯﷯ . 𝑑𝑡 = 𝑒﷮𝑡﷯+𝐶 = 𝒆﷮ 𝒕𝒂𝒏﷮−𝟏﷯ 𝒙﷯+𝑪

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