Posted by abhi on Friday, October 5, 2012 at 12:30pm.
this one is a bit less complicated than the last one.
∫x^2/√(x-1)
Let u^2 = x-1
2u du = dx
x = 1+u^2
and we have
∫(1+u^2)^2/u 2u du
2∫(1+u^2)^2 du
2∫1 + 2u^2 + u^4 du
2(u + 2/3 u^3 + 1/5 u^5)
2/15 √(x-1)(15 + 10(x-1) + 3(x-1)^2)
2/15 √(x-1)(15 + 10x - 10 + 3x^2 - 6x + 3)
2/15 √(x-1) (3x^2 + 4x + 8)
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