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Misc 4 - Integrate 1 / x2 (x4 + 1)3/4 - Class 12 NCERT - Miscellaneous

Misc 4 - Chapter 7 Class 12 Integrals - Part 2
Misc 4 - Chapter 7 Class 12 Integrals - Part 3


Transcript

Misc 4 Integrate the function 1﷮ 𝑥﷮2﷯ 𝑥﷮4﷯ + 1﷯﷮ 3﷮4﷯﷯ ﷯ ﷮﷮ 1 𝑑𝑥﷮ 𝑥﷮2﷯ 𝑥﷮4﷯ + 1﷯﷮ 3﷮4﷯﷯ ﷯﷯ Taking 𝒙﷮𝟒﷯ common from denominator = ﷮﷮ 1 𝑑𝑥﷮ 𝑥﷮2 ﷯ (𝑥﷮4﷯)﷮ 3﷮4﷯﷯ 1 + 1﷮ 𝑥﷮4﷯﷯﷯﷮ 3﷮4﷯﷯﷯﷯ = ﷮﷮ 𝑑𝑥﷮ 𝑥﷮2﷯ (𝑥﷮3﷯) 1 + 1﷮ 𝑥﷮4﷯﷯﷯﷮ 3﷮4﷯﷯﷯﷯ = ﷮﷮ 𝑑𝑥﷮ 𝑥﷮5﷯ 1 + 1﷮ 𝑥﷮4﷯﷯﷯﷮ 3﷮4﷯﷯﷯﷯ Let t = 1 + 1﷮ 𝑥﷮4﷯﷯ 𝑑𝑡﷮𝑑𝑥﷯ = − 4﷮ 𝑥﷮5﷯﷯ − 𝑑𝑡﷮4﷯ = 𝑑𝑥﷮ 𝑥﷮5﷯﷯ Substituting value of x and dx = −1﷮4﷯ ﷮﷮ 𝑑𝑡﷮ 𝑡﷮ 3﷮4﷯﷯﷯﷯ = −1﷮4﷯ ﷮﷮ 𝑡﷮ −3﷮4﷯﷯﷯ 𝑑𝑡 = −1﷮4﷯ 𝑡﷮ −3﷮4﷯ + 1﷯﷮ −3﷮4﷯ + 1﷯﷯+ C = −1﷮4﷯ 𝑡﷮ 1﷮4﷯﷯﷮ 1﷮4﷯﷯﷯+ C = − 𝑡﷮ 1﷮4﷯﷯+ C = − 𝟏+ 𝟏﷮ 𝒙﷮𝟒﷯﷯﷯﷮ 𝟏﷮𝟒﷯﷯+ C

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.