Primitive of Arccosine Function

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Theorem

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


Proof

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

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

The result follows by setting $a = 1$.

$\blacksquare$


Also see


Sources