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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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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 is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.