

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class
Miscellaneous
Misc 2 Important
Misc 3 Important
Misc 4
Misc 5 Important
Misc 6
Misc 7 Important
Misc 8 Important
Misc 9
Misc 10 Important
Misc 11
Misc 12
Misc 13
Misc 14 Important
Misc 15
Misc 16
Misc 17
Misc 18 Important
Misc 19 Important
Misc 20
Misc 21
Misc 22 You are here
Misc 23 Important
Misc 24 Important
Misc 25 Important
Misc 26 Important
Misc 27 Important
Misc 28
Misc 29 Important
Misc 30 Important
Misc 31 Important
Misc 32
Misc 33
Misc 34
Misc 35
Misc 36 Important
Misc 37
Misc 38 (MCQ) Important
Misc 39 (MCQ)
Misc 40 (MCQ)
Integration Formula Sheet - Chapter 41 Class 41 Formulas Important
Question 1 Important Deleted for CBSE Board 2024 Exams
Question 2 Important Deleted for CBSE Board 2024 Exams
Question 3 Important Deleted for CBSE Board 2024 Exams
Question 4 (MCQ) Important Deleted for CBSE Board 2024 Exams
Last updated at May 29, 2023 by Teachoo
Misc 22 Integrate the function tan−1 1 − 𝑥1 + 𝑥 Let x = cos 2𝜃 𝑑𝑥𝑑𝜃=−2 sin2𝜃 dx = −2 sin 2𝜃 d𝜃 Substituting, tan−1 1 − 𝑥1 + 𝑥 𝑑𝑥 = 𝑡𝑎𝑛−1 1 − cos2𝜃1 + cos2𝜃×(−2 sin2 𝜃) 𝑑 𝜃 = −2 𝑡𝑎𝑛−1 1 − 1 − 2 𝑠𝑖𝑛2 𝜃1 + 2 𝑐𝑜𝑠2 𝜃 − 1× sin 2𝜃 d𝜃 = −2 𝑡𝑎𝑛−1 sin2𝜃 cos2𝜃× sin2𝜃 𝑑𝜃 = −2 𝑡𝑎𝑛−1 sin𝜃 cos𝜃× sin2𝜃 𝑑𝜃 = −2 𝑡𝑎𝑛−1 𝑡𝑎𝑛𝜃× sin2𝜃 𝑑𝜃 = − 2 𝜃 sin2𝜃 𝑑𝜃 =−2 𝜃 sin2𝜃 𝑑𝜃− 𝑑 𝜃𝑑𝜃 sin2𝜃 𝑑𝜃 𝑑𝜃 =−2 𝜃 − cos2𝜃2− 1 − cos2𝜃2𝑑𝜃 =−2 −𝜃 cos2𝜃2+ cos2𝜃2𝑑𝜃 =−2 − 𝜃 cos2𝜃2+ sin2𝜃4 Now, x = cos 2𝜃 Putting the values = −2 − 12 12 𝑐𝑜𝑠−1𝑥𝑥+ 1 − 𝑥24 = −2 1 − 𝑥24− 𝑥 𝑐𝑜𝑠−1𝑥4+ C = 𝟏𝟐 𝒙 𝒄𝒐𝒔−𝟏𝒙− 𝟏− 𝒙𝟐 + C