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1. The question is: using the substitution find: the integrl of (x/((x+a)^0.5)). The answer in the book is 2/3(x-2)((x+1)^0.5)) but i keep getting 2/3((x+1)^1.5)) - 2((x+1)^0.5). Both soultions give the same anwers whe i substitute a value of x in, but would i be penalised for giving the differnt answer? Thanks!!
2. sorry, the substitution is t^2 = x + 1
3. They are in essence the same answer.
2/3((x+1)^1.5)) - 2((x+1)^0.5)
= (x+1)^0.5 [ 2/3(x+1) -2]
= (x+1)^0.5 [ 2/3x+ 2/3 -2]
=(x+1)^0.5 [ 2/3x -4/3] = (x+1)^0.5 [ 2/3(x-2)]
= 2/3 (x-2) (x+1)^0.5

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Updated: June 11, 2006
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