Primitive of Reciprocal of Root of x squared plus a squared/Logarithm Form

Theorem

 * $\ds \int \frac {\d x} {\sqrt {x^2 + a^2} } = \map \ln {x + \sqrt {x^2 + a^2} } + C$

Also presented as
Some sources present this in the form:


 * $\ds \int \frac {\d x} {\sqrt {x^2 + a^2} } = \map \ln {\dfrac {x + \sqrt {x^2 + a^2} } a} + C$

which is the same as above, except that the constant $a$ has not been subsumed into the arbitrary constant $C$.

Also see

 * Primitive of $\dfrac 1 {\sqrt {x^2 - a^2} }$: Logarithm Form
 * Primitive of $\dfrac 1 {\sqrt {a^2 - x^2} }$