Primitive of Arcsine Function

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Theorem

$\ds \int \arcsin x \rd x = x \arcsin x + \sqrt {1 - x^2} + C$


Proof

From Primitive of $\arcsin \dfrac x a$:

$\ds \int \arcsin \frac x a \rd x = x \arcsin \frac x a + \sqrt {a^2 - x^2} + C$

The result follows by setting $a = 1$.

$\blacksquare$


Also see


Sources