Question 19

Find: ∫ (x 4   + 1) / x (x 2   + 1) 2  dx

Find Integration (x^4  + 1) / x (x^2  + 1)^2 - Teachoo - CBSE Class 12

Question 19 - CBSE Class 12 Sample Paper for 2019 Boards - Part 2
Question 19 - CBSE Class 12 Sample Paper for 2019 Boards - Part 3

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

Question 19 Find: ∫1▒(𝑥^4 + 1)/(𝑥(𝑥^2 + 1)^2 ) dx ∫1▒(𝑥^4 + 1)/(𝑥(𝑥^2 + 1)^2 ) dx Writing x4 +1 = x4 + 1 + 2x2 – 2x2 ∫1▒(𝑥^4 + 1)/(𝑥(𝑥^2 + 1)^2 ) dx = ∫1▒(𝑥^4 + 1 + 2𝑥^2 − 2𝑥^2)/(𝑥(𝑥^2 + 1)^2 ) dx = ∫1▒((𝑥^2 + 1)^2 − 2𝑥^2)/(𝑥(𝑥^2 + 1)^2 ) dx = ∫1▒(𝑥^2 + 1)^2/(𝑥(𝑥^2 + 1)^2 ) dx – ∫1▒(2𝑥^2)/(𝑥(𝑥^2 + 1)^2 ) dx = ∫1▒1/𝑥 dx – ∫1▒2𝑥/(𝑥^2 + 1)^2 dx = log⁡〖|𝑥|〗 – ∫1▒2𝑥/(𝑥^2 + 1)^2 dx Let x2 + 1 = t 2x dx = dt = log⁡〖|𝑥|〗 – ∫1▒𝑑𝑡/𝑡^2 = log⁡〖|𝑥|〗 – 𝑡^(−2 + 1)/(−2 + 1) + C = log⁡〖|𝑥|〗 – 𝑡^(−1)/(−1) + C = log⁡〖|𝑥|〗 + 1/t + C Putting back t = x2 + 1 = log⁡〖|𝑥|〗 + 1/(x^2 + 1) + 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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.