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Example 38 - Evaluate integral (x4 - x)1/4 / x5 dx - Examples

Example 38 - Chapter 7 Class 12 Integrals - Part 2


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Example 38 Evaluate ∫1β–’(π‘₯^4 βˆ’π‘₯)^(1/4)/π‘₯^5 𝑑π‘₯ ∫1β–’(π‘₯^4 βˆ’ π‘₯)^(1/4)/π‘₯^5 𝑑π‘₯ Taking π‘₯^4 common from numerator =∫1β–’γ€–(π‘₯^4 )^(1/4) (1 βˆ’ π‘₯/π‘₯^4 )γ€—^(1/4)/π‘₯^5 𝑑π‘₯ = ∫1β–’(π‘₯ (1 βˆ’ 1/π‘₯^3 )^(1/4))/π‘₯^5 𝑑π‘₯ = ∫1β–’(1 βˆ’ 1/π‘₯^3 )^(1/4)/π‘₯^4 𝑑π‘₯ Let t = 1 βˆ’ 1/π‘₯^3 𝑑𝑑/𝑑π‘₯=3/π‘₯^4 Substituting values, =∫1▒〖𝑑 γ€—^(1/4)/3 𝑑𝑑 = 1/3 (𝑑^( 1/(4 ) + 1)/(1/4 +1))+ C = 1/3 ((𝑑^( 5/4) )/(5/4))+ C = 4/15 〖𝑑 γ€—^(5/4)+ C = πŸ’/πŸπŸ“ (πŸβˆ’πŸ/𝒙^πŸ‘ )^( πŸ“/πŸ’)+ C

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.