Ex 7.2, 36 - Integrate (x + 1) (x + log x)2 / x - Integration by substitution - lnx

Slide13.JPG

  1. Class 12
  2. Important Question for exams Class 12
Ask Download

Transcript

Ex 7.2, 36 ((π‘₯ + 1) (π‘₯ + log⁑π‘₯ )^2)/π‘₯ Step 1: Let π‘₯+log⁑π‘₯= 𝑑 Differentiating both sides 𝑀.π‘Ÿ.𝑑.π‘₯ 1+1/π‘₯= 𝑑𝑑/𝑑π‘₯ (π‘₯ + 1)/π‘₯= 𝑑𝑑/𝑑π‘₯ " " 𝑑π‘₯ = ((π‘₯ )/(π‘₯ + 1))𝑑𝑑 Step 2: Integrating the function ∫1β–’γ€–" " ((π‘₯ + 1) (π‘₯ + log⁑π‘₯ )^2)/π‘₯γ€— . 𝑑π‘₯ Putting the value of π‘₯βˆ’π‘™π‘œπ‘”β‘π‘₯=𝑑 & 𝑑π‘₯=((π‘₯ )/(π‘₯ + 1))𝑑𝑑 = ∫1β–’γ€–" " ((π‘₯ + 1) (𝑑)^2)/π‘₯γ€— . (π‘₯ )/((π‘₯ + 1) ) . 𝑑𝑑 = ∫1β–’γ€–" " 𝑑^2 γ€—. 𝑑𝑑" " = 𝑑^(2 + 1)/(2 + 1) +𝐢 = 𝑑^3/3 +𝐢 = 𝟏/πŸ‘ (𝒙+π’π’π’ˆβ‘π’™ )^πŸ‘+π‘ͺ

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 7 years. He provides courses for Mathematics and Science from Class 6 to 12. You can learn personally from here https://www.teachoo.com/premium/maths-and-science-classes/.
Jail