Integral from 0 to 1 of 1/sqrt(1+x^2)

1. Jan 17, 2009

uman

1. The problem statement, all variables and given/known data
$$\int_0^1 \frac{1}{\sqrt{x^2+1}}\,dx$$

2. Relevant equations
Integration by substitution looks like it might help here...

3. The attempt at a solution
The answer is $$\log (1+\sqrt 2)$$, but I'm at a loss as to how to derive that.

2. Jan 17, 2009

rock.freak667

You could try a trig substitution such as $x=tan\theta$.Hyperbolic trig sub. would be possible as well.

3. Jan 17, 2009

uman

Thanks. I worked it out using your suggestion, but x = sinh(theta) also works, in case anyone cares. :-)