Primitive of Reciprocal of Root of a squared minus x squared
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Theorem
Primitive of $\dfrac 1 {\sqrt {a^2 - x^2} }$: $\arcsin$ form
- $\ds \int \frac {\d x} {\sqrt {a^2 - x^2} } = \arcsin \frac x a + C$
Primitive of $\dfrac 1 {\sqrt {a^2 - x^2} }$: $\arccos$ form
- $\ds \int \frac 1 {\sqrt {a^2 - x^2} } \rd x = -\arccos \frac x a + C$
Examples
Primitive of $\dfrac 1 {\sqrt {16 - x^2} }$
- $\ds \int \dfrac 1 {\sqrt {16 - x^2} } \rd x = \arcsin \dfrac x 4 + C$