Question 19 - CBSE Class 12 Sample Paper for 2019 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at April 16, 2024 by Teachoo

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

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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 14 years. He provides courses for Maths, Science and Computer Science at Teachoo

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