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Ex 7.4, 9 - Integrate sec2 x / root tan2 x + 4 - Integration by specific formulaes - Formula 6

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Ex 7.4, 9 sec﷮2﷯﷮𝑥﷯﷮ ﷮ tan﷮2﷯﷮𝑥 + 4﷯﷯﷯ Let tan﷮𝑥﷯=𝑡 Diff both sides w.r.t. x sec﷮2﷯﷮𝑥﷯= 𝑑𝑡﷮𝑑𝑥﷯ 𝑑𝑥= 𝑑𝑡﷮ sec﷮2﷯﷮𝑥﷯﷯ Integrating the function 𝑤.𝑟.𝑡.𝑥 ﷮﷮ sec﷮2﷯﷮𝑥﷯﷮ ﷮ tan﷮2﷯﷮𝑥 + 4﷯﷯﷯﷯ Putting value of tan 𝑥=𝑡 and 𝑑𝑥= 𝑑𝑡﷮ sec﷮2﷯﷮𝑥﷯﷯ = ﷮﷮ sec﷮2﷯﷮𝑥﷯﷮ ﷮ t﷮2﷯﷮+ 4﷯﷯﷯﷯ . 𝑑𝑡﷮ sec﷮2﷯﷮𝑥﷯﷯ = ﷮﷮ 1﷮ ﷮ t﷮2﷯﷮+ 4﷯﷯﷯﷯ . 𝑑𝑡 = ﷮﷮ 1﷮ ﷮ t﷮2﷯﷮+ 2﷯﷮2﷯﷯﷯﷯﷯ . 𝑑𝑡 = log﷮ 𝑡+ ﷮ 𝑡﷮2﷯ + 2﷯﷮2﷯﷯﷯﷯+𝐶 = log﷮ 𝑡+ ﷮ 𝑡﷮2﷯ +4﷯﷯﷯+𝐶 = 𝒍𝒐𝒈﷮ 𝒕𝒂𝒏﷮𝒙﷯+ ﷮ 𝒕𝒂𝒏﷮𝟐﷯𝒙 +𝟒﷯ ﷯﷯+𝑪

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