Breaking up an integral using substitution? I am faced with the following integral, and am required to use substitution to solve it, using $u = \frac{1}{x}$. 
$$\int \dfrac{1}{x^2\sqrt{x^2+1}} \, dx$$
I know I can break up the equation in:
$$\int \dfrac{1}{x}\dfrac{1}{x}\dfrac{1}{\sqrt{x^2+1}} \, dx.$$
How would I go about replacing the variable $x$ in the sqrt though? 

I suggest you to use $$\frac{\sqrt{1+x^2}}{x}=t$$ So you 'll find the integral reduced to the following one: $$\int -dt$$
