Evaluate: `int1/((x^2-4)sqrt(x+1))dx`

Explanation

`x=t^2-1=>dx=2tdt`

`I= 2int frac{1}{(t^2-1)^2-4}dt`

`= 2int frac{dt}{(t^2-1-2)(t^2-1+2)} `

`2 int frac{dt}{(t^2-3)(t^2-1)}`

`1/((y-3)(y-1))=frac{A}{y-3}+frac{B}{y+1}`

`A=(1/4) ` and `B=(-1/4)`

`I=2/4 int frac{1}{t^2-3}-frac{1}{t^2+1}dt`

`=1/(4 sqrt 3) log abs(frac{t- sqrt 3}{t+ sqrt3})-1/2 tan^(-1)t+C`
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