Ex 7.4, 8 - Integrate x2 / root x6 + a6

Ex 7.4, 8 𝑥﷮2﷯﷮ ﷮ 𝑥﷮6﷯ + 𝑎﷮6﷯﷯﷯ 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 ﷮﷮ 𝑥﷮2﷯﷮ ﷮ 𝑥﷮6﷯ + 𝑎﷮6﷯﷯﷯﷯ 𝑑𝑥= ﷮﷮ 𝑥﷮2﷯﷮ ﷮ 𝑥﷮3﷯﷯﷮2﷯ + 𝑎﷮3﷯﷯﷮2﷯﷯﷯﷯ 𝑑𝑥 Putting values of 𝑥﷮3﷯=𝑡 and 𝑑𝑥= 𝑑𝑡﷮3 𝑥﷮2﷯﷯ , we get = ﷮﷮ 𝑥﷮2﷯﷮ ﷮ 𝑡﷮2﷯ + 𝑎﷮3﷯﷯﷮2﷯﷯﷯﷯ 𝑑𝑥 = ﷮﷮ 𝑥﷮2﷯﷮ ﷮ 𝑡﷮2﷯ + 𝑎﷮3﷯﷯﷮2﷯﷯﷯﷯ . 𝑑𝑡﷮3 𝑥﷮2﷯﷯ = ﷮﷮ 1﷮ ﷮ 𝑡﷮2﷯ + 𝑎﷮3﷯﷯﷮2﷯﷯ ﷯﷯﷯ . 𝑑𝑡﷮3﷯ = 1﷮3﷯ ﷮﷮ 𝑑𝑡﷮ ﷮ 𝑡﷮2﷯ + 𝑎﷮3﷯﷯﷮2﷯﷯﷯﷯ = 1﷮3﷯ log﷮ 𝑡+ ﷮ 𝑡﷮2﷯ + 𝑎﷮3﷯﷯﷮2﷯﷯﷯﷯+𝐶1﷯ = 1﷮3﷯ log﷮ 𝑡+ ﷮ 𝑡﷮2﷯ + 𝑎﷮6﷯﷯ ﷯﷯+𝐶 = 1﷮3﷯ log﷮ 𝑥﷮3﷯+ ﷮ 𝑥﷮3﷯﷯﷮2﷯ + 𝑎﷮6﷯﷯ ﷯﷯+𝐶 = 𝟏﷮𝟑﷯ 𝒍𝒐𝒈﷮ 𝒙﷮𝟑﷯+ ﷮ 𝒙﷮𝟔﷯+ 𝒂﷮𝟔﷯﷯ ﷯﷯+𝑪

Ex 7.4, 8 - Chapter 7 Class 12 Integrals