Question 19
Find: ∫ (x ^{ 4 } + 1) / x (x ^{ 2 } + 1) ^{ 2 } dx
Last updated at Oct. 1, 2019 by Teachoo
Question 19
Find: ∫ (x ^{ 4 } + 1) / x (x ^{ 2 } + 1) ^{ 2 } dx
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
CBSE Class 12 Sample Paper for 2019 Boards
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CBSE Class 12 Sample Paper for 2019 Boards
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