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

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

This result is also seen presented in the form:

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

This needs considerable tedious hard slog to complete it. In particular: Somebody with an eye to detail may wish to establish under what conditions is the absolute value important To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Finish}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Sources

• 1968: George B. Thomas, Jr.: Calculus and Analytic Geometry (4th ed.) ... (previous) ... (next): Front endpapers: A Brief Table of Integrals: $34$.