The integral ∫▒dx/((x+1)^(3/4) (x-2)^(5/4) ) is equal to

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The integral ∫▒dx/((x+1)^(3/4) (x-2)^(5/4) ) is equal to
(a) 4((x+1)/(x-2))^(1/4)+C (b) 4((x-2)/(x+1))^(1/4)+C
(c) -4/3 ((x+1)/(x-2))^(1/4)+C (d) -4/3 ((x-2)/(x+1))^(1/4)+C
Ans: c
Sol.
Let I=∫▒dx/((x+1)^(3/4) (x-2)^(5/4) )
=∫▒dx/(((x+1)/(x-2))^(3/4) (x-2)^2 )
Put (x+1)/(x-2)=t⇒(-3)/(x-2)^2 =dt/dx
So, I=∫▒dt/(-3t^(3/4) )=(-1)/3 (t^((-3)/4+1)/((-3)/4+1))
=(-4)/3 t^(1/4)+C=(-4)/3 ((x+1)/(x-2))^(1/4)+C

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