# I don't like memorizing

1. Feb 26, 2009

### orthovector

does anybody know how to derive this integral???

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

Last edited: Feb 26, 2009
2. Feb 26, 2009

### Dick

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

3. Feb 26, 2009

### orthovector

corrections are made above.

4. Feb 26, 2009

### 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).

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