Primitive of Reciprocal of x by Root of x squared plus a squared/Logarithm Form/Also presented as

Primitive of $\frac 1 {x \sqrt {x^2 + a^2} }$: Logarithm Form: Also presented as

This result is also seen presented in the form:

$\ds \int \frac {\d x} {x \sqrt {x^2 + a^2} } = -\frac 1 a \ln \size {\frac a x + \frac {\sqrt {a^2 + x^2} } x} + C$

Sources

• 1968: George B. Thomas, Jr.: Calculus and Analytic Geometry (4th ed.) ... (previous) ... (next): Front endpapers: A Brief Table of Integrals: $26$.