<s>[INST] Calculate the indefinite integral $\int \frac{dx}{({x^2-2x+5})^\frac{3}{2}} $ I have this.
$$\int \frac{dx}{({x^2-2x+5})^\frac{3}{2}} $$
I tried to define -
$ u = x-1 $
$\int \frac{du}{8(\frac{u^2}{4}+1)^{\frac{3}{2}}} = \frac{1}{8}\int \frac{du}{(\frac{u^2}{4}+1)^{\frac{3}{2}}}$
Now, im pretty stuck.
Thanks.
 [/INST] Hint...substitute $x=1+2\tan\theta$
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