<s>[INST] Indefinite Integration : $\int \frac{dx}{(x+\sqrt{(x^2-1)})^2}$ Problem : 
Solve : $\int \frac{dx}{(x+\sqrt{(x^2-1)})^2}$......(i) 
I tried : 
Let $x =\sec\theta$ therefore , (i) will become after some simplification 
$$\int \frac{\sin\theta}{(1+\sin\theta)^2}d\theta$$
but i think its wrong method of approaching please suggest further....thanks..
 [/INST] HINT: $$\frac1{x+\sqrt{x^2-1}}=x-\sqrt{x^2-1}$$
So, $$\frac1{(x+\sqrt{x^2-1})^2}=(x-\sqrt{x^2-1})^2=x^2+x^2-1-2x\sqrt{x^2-1}=2x^2-1-2x\sqrt{x^2-1}$$
Put $x^2-1=y$ for the last part
</s>