Ex 7.4, 1 - Integrate 3x2 / x6 + 1 - Chapter 7 Class 12 - Ex 7.4

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Ex 7.4, 1 3 𝑥﷮2﷯﷮ 𝑥﷮6﷯ + 1﷯ Let 𝑥﷮3﷯=𝑡 Diff both sides w.r.t.x 3 𝑥﷮2﷯= 𝑑𝑡﷮𝑑𝑥﷯ 𝑑𝑥= 𝑑𝑡﷮3 𝑥﷮2﷯﷯ Step :- 2 Integrating the function 𝑤.𝑟.𝑡.𝑥 ﷮﷮ 3 𝑥﷮2﷯﷮ 𝑥﷮6﷯ + 1﷯﷯ 𝑑𝑥 = ﷮﷮ 3 𝑥﷮2﷯﷮ 𝑥﷮3﷯﷯﷮2﷯ + 1﷯﷯ 𝑑𝑥 Putting the value of 𝑥﷮3﷯ and 𝑑𝑥= 𝑑𝑡﷮3 𝑥﷮2﷯﷯ = ﷮﷮ 3 𝑥﷮2﷯﷮ 𝑡﷮2﷯ + 1﷯﷯ . 𝑑𝑡﷮3 𝑥﷮2﷯﷯ = ﷮﷮ 𝑑𝑡﷮ 𝑡﷮2﷯ + 1﷯﷯ = ﷮﷮ 𝑑𝑡﷮ 𝑡﷮2﷯ + 1﷯﷮2﷯﷯﷯ = 1﷮1﷯ tan﷮−1﷯﷮ 𝑡﷮1﷯ ﷯+𝐶 = tan﷮−1﷯﷮ 𝑡﷯﷯+𝐶 = 𝒕𝒂𝒏﷮−𝟏﷯ ﷮ 𝒙﷮𝟑﷯﷯﷯+𝑪

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