1st problem is nice I will tell you the general way of solving these problems
It is the type of problems where
x m ( a + bx n ) p ,
Now here you have m = - 3 , n = 1 , p = 2
In these type of problems you have, (m+1)/n = an integer , so you can try putting
( a + b x n ) part = t k where k is the denominator of the fraction p
now replace it as said and you will see its easy ,
It now reduces to
2 t dt / t ( t2 + 1 ) = 2 dt / (t 2 + 1) 3
Now make required substitutions and get the answer.....this is the approach.
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34
dx/x^3(x-1)^1/2 = (x-1)^1/2 (3x+2)/4x^2 +K tan^(-1)rt(x-1) +C
dt / (t 2 + 1) 3 
