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integral of : x^2 square root of (x-1)

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Put x = y+1

Integral of x^2 sqrt(x-1) dx

= Integral of (y+1)^2 sqrt(y)dy =

Integral of [y^(5/2) + 2 y^(3/2) +
y^(1/2)]dy

= 2/7 y^(7/2) + 4/5 y^(5/2)
+ 2/3 y^(3/2)

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