Primitive of Reciprocal of Root of x squared minus a squared/Logarithm Form/Also presented as
Jump to navigation
Jump to search
Primitive of $\frac 1 {\sqrt {x^2 - a^2} }$: Logarithm Form: Also presented as
The standard presentation of this result is:
- $\ds \int \frac {\d x} {\sqrt {x^2 - a^2} } = \ln \size {x + \sqrt {x^2 - a^2} } + C$
for $0 < a < \size x$.
Some sources present this in the form:
- $\ds \int \frac {\d x} {\sqrt {x^2 - a^2} } = \ln \size {\dfrac {x + \sqrt {x^2 - a^2} } a} + C$
which is the same as above, except that the constant $a$ has not been subsumed into the arbitrary constant $C$.
Sources
- 1945: A. Geary, H.V. Lowry and H.A. Hayden: Advanced Mathematics for Technical Students, Part I ... (previous) ... (next): Chapter $\text {III}$: Integration: Integration
- 1960: Margaret M. Gow: A Course in Pure Mathematics ... (previous) ... (next): Chapter $10$: Integration: $10.4$. Standard integrals: Standard Forms: $\text {(xi)}$
- 1976: K. Weltner and W.J. Weber: Mathematics for Engineers and Scientists ... (previous) ... (next): $6$. Integral Calculus: Appendix: Table of Fundamental Standard Integrals