Please help me find my mistake in this integration

[Dell]

$$\int$$dx/x*(x²-1)^0.5 (from 1 to infinity)

i said t=(x²-1)^0.5, therefore x²=t²+1
dt=x/(x²-1)^0.5

so now i have

$$\int$$dx/x*(x²-1)^0.5=$$\int$$xdx/x²*(x²-1)^0.5=$$\int$$dt/x²=$$\int$$dt/t+1 (now integral from 0 to infinity)

$$\int$$dt/t+1 (from 0 to infinity)

=lim arctan(t)$$^{b}_{0}$$=pi/4
b-inf


but the correct answer is pi/2, can ANYONE see where i have gone wrong?

 

[Cyosis]

You didn't adjust your limits after the substitution. If $t=\sqrt{x^2-1}$ and x goes from 1 to infinity then t goes from 0 to infinity.

ps. It would be nice if you use brackets properly so we don't have to guess which function is actually being integrated.

 

[Dell]

if you look at the 5th line of text youll see that i did change my limits,

 

[Cyosis]

I missed that, still are you sure you didn't use the old limits? As they yields pi/4. So what's arctan(0) and what's arctan(x) with x going to infinity? Hint: your mistake has to do with filling in the limits.