How can I easily derive this tricky integral?

[orthovector]

does anybody know how to derive this integral?

$$\int \frac{dx}_{\sqrt{x^2 + a^2}}$$ $$= ln(x+ \sqrt{x^2 + a^2})$$

 

[Dick]

Looks like you already took it, wrongly. Looks more to me like an arctan. Some things are worth memorizing. Not all, but some.

 

[orthovector]

Looks like you already took it, wrongly. Looks more to me like an arctan. Some things are worth memorizing. Not all, but some.

corrections are made above.

 

[Dick]

The easy way is to use hyperbolic functions. Substitute x=a*sinh(t). Then figure out what the arcsinh function looks like by solving a quadratic. Otherwise a trig substitution like x=a*tan(t).