Ex 7.4, 6

Last updated at Dec. 8, 2016 by Teachoo

Ex 7.4, 6 - Integrate x2 / 1 - x6 - Chapter 7 CBSE NCERT - Ex 7.4

Transcript

Ex 7.4, 6 𝑥2/(1 − 𝑥6) Let 𝑥^3=𝑡 Diff both sides w.r.t. x 3𝑥^2=𝑑𝑡/𝑑𝑥 𝑑𝑥=𝑑𝑡/(3𝑥^2 ) Integrating the function 𝑤.𝑟.𝑡.𝑥 ∫1▒𝑥^2/(1 − 𝑥^6 ) 𝑑𝑥 =∫1▒𝑥^2/(1 − (𝑥^3 )^2 ) 𝑑𝑥 Put the values of 𝑥^3=𝑡 and 𝑑𝑥=𝑑𝑡/(3𝑥^2 ) =∫1▒𝑥^2/(1 − 𝑡^2 ) . 𝑑𝑥 =∫1▒𝑥^2/(1 − 𝑡^2 ) × 𝑑𝑡/(3𝑥^2 ) =1/3 ∫1▒𝑑𝑡/(1 − 𝑡^2 ) =1/3 ∫1▒𝑑𝑡/((1)^2 − 𝑡^2 ) =1/3 [1/2(1) log⁡|(1 + 𝑡)/(1 − 𝑡)| ]+𝐶 =1/6 log⁡|(1 + 𝑡)/(1 − 𝑡)|+𝐶 =𝟏/𝟔 𝒍𝒐𝒈⁡|(𝟏 + 𝒙^𝟑)/(𝟏 − 𝒙^𝟑 )|+𝑪

Ex 7.4

Ex 7.4, 6 You are here

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