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integration of (1/((x-1)^3/4 (x+2)^5/4)))=?

integration of (1/((x-1)^3/4 (x+2)^5/4)))=?

Grade:12th pass

1 Answers

Rinkoo Gupta
askIITians Faculty 80 Points
7 years ago
integral (1/(x-a)^3/4(x+2)^5/4)dx
let x-1=1/t
dx=-dt/t^2
then integral become
integral (-1/t^2).(t^3/4)dt/(1/t+3)
=-integral dt/(1+3t)5/4
=-integral(3t+1)^(-5/4) dt
=(4/3).1/(3t+1)^(1/4)
=(4/3).1/(3/(x-1)+1)^(1/4)
=(4/3)[(x-1)/(x+2)]^1/4 Ans.

Thanks & Regards
Rinkoo Gupta
AskIITians Faculty

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